[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/16030#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/16030","headline":"Pettis Integral -Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","name":"Pettis Integral -Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206 a\u3002 Gelfanda-Pettisa &#8211; \u691c\u8a0e\u4e2d\u306e\u4e00\u5b9a\u306e\u7dda\u5f62\u95a2\u6570\u3092\u6301\u3064\u7d61\u307f\u5408\u3063\u305f\u95a2\u6570\u306e\u554f\u984c\u306b\u3082\u305f\u3089\u3059\u3053\u3068\u306b\u3088\u308a\u3001\u7dda\u5f62\u30c8\u30d4\u30ab\u30eb\u30b9\u30da\u30fc\u30b9\u5185\u306e\u5024\u3092\u6301\u3064\u7a4d\u5206\u306e\u6982\u5ff5\u306e\u62e1\u5f35\u3002\u3053\u306e\u5834\u5408\u3001\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u76f8\u4e92\u4f5c\u7528\u306e\u554f\u984c\u306f\u30013\u3064\u306e\u8981\u56e0\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u95a2\u6570\u304c\u6307\u5b9a\u3055\u308c\u3066\u3044\u308b\u5c3a\u5ea6\u3001\u5024\u81ea\u4f53\u306e\u5024\u306e\u6240\u6709\u6a29\u3001\u304a\u3088\u3073\u9023\u7d9a\u7dda\u5f62\u95a2\u6570\u306e\u5f62\u5f0f\u3092\u4f34\u3046\u7a7a\u9593\u306e\u6240\u6709\u3002\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u7d71\u5408\u306f\u3001\u30d9\u30af\u30c8\u30eb\u5024\u3092\u6301\u3064\u95a2\u6570\u306e\u7d71\u5408\u6027\u306e\u4e00\u822c\u5316\u306e\u53ef\u80fd\u6027\u306e1\u3064\u306b\u3059\u304e\u306a\u3044\u3053\u3068\u306b\u7559\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ed6\u306e\u305d\u306e\u3088\u3046\u306a\u4e00\u822c\u5316\u306b\u306f\u3001\u3068\u308a\u308f\u3051\u304c\u542b\u307e\u308c\u307e\u3059Birkhoff\u306e\u7a4d\u5206\u3001McShane\u306e\u7a4d\u5206\u3001Dunford\u306e\u7a4d\u5206\u3001\u307e\u305f\u306fBochner\u306e\u7a4d\u5206\u3002\u6982\u5ff5\u306e\u540d\u524d\u306f\u3001\u6570\u5b66\u8005I. M. Gelfanda\u3068B.J.\u306e\u540d\u524d\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059\u3002\u30da\u30c6\u30a3\u30b5\u3002 after-content-x4 \u3055\u305b\u3066 \uff08 \u304a\u304a \u3001 a \u3001 m \uff09\uff09 {displaystyle\uff08omega\u3001{mathcal {a}}\u3001mu\uff09} \u305d\u308c\u306f\u5c3a\u5ea6\u306e\u5c3a\u5ea6\u306b\u306a\u308a\u3001","datePublished":"2020-02-25","dateModified":"2020-02-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/3cabc7dd1ffb04becc182e5356682ec027db7211","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/3cabc7dd1ffb04becc182e5356682ec027db7211","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/16030","wordCount":8462,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u30da\u30c6\u30a3\u30b9\u7a4d\u5206 a\u3002 Gelfanda-Pettisa  &#8211; \u691c\u8a0e\u4e2d\u306e\u4e00\u5b9a\u306e\u7dda\u5f62\u95a2\u6570\u3092\u6301\u3064\u7d61\u307f\u5408\u3063\u305f\u95a2\u6570\u306e\u554f\u984c\u306b\u3082\u305f\u3089\u3059\u3053\u3068\u306b\u3088\u308a\u3001\u7dda\u5f62\u30c8\u30d4\u30ab\u30eb\u30b9\u30da\u30fc\u30b9\u5185\u306e\u5024\u3092\u6301\u3064\u7a4d\u5206\u306e\u6982\u5ff5\u306e\u62e1\u5f35\u3002\u3053\u306e\u5834\u5408\u3001\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u76f8\u4e92\u4f5c\u7528\u306e\u554f\u984c\u306f\u30013\u3064\u306e\u8981\u56e0\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u95a2\u6570\u304c\u6307\u5b9a\u3055\u308c\u3066\u3044\u308b\u5c3a\u5ea6\u3001\u5024\u81ea\u4f53\u306e\u5024\u306e\u6240\u6709\u6a29\u3001\u304a\u3088\u3073\u9023\u7d9a\u7dda\u5f62\u95a2\u6570\u306e\u5f62\u5f0f\u3092\u4f34\u3046\u7a7a\u9593\u306e\u6240\u6709\u3002\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u7d71\u5408\u306f\u3001\u30d9\u30af\u30c8\u30eb\u5024\u3092\u6301\u3064\u95a2\u6570\u306e\u7d71\u5408\u6027\u306e\u4e00\u822c\u5316\u306e\u53ef\u80fd\u6027\u306e1\u3064\u306b\u3059\u304e\u306a\u3044\u3053\u3068\u306b\u7559\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ed6\u306e\u305d\u306e\u3088\u3046\u306a\u4e00\u822c\u5316\u306b\u306f\u3001\u3068\u308a\u308f\u3051\u304c\u542b\u307e\u308c\u307e\u3059Birkhoff\u306e\u7a4d\u5206\u3001McShane\u306e\u7a4d\u5206\u3001Dunford\u306e\u7a4d\u5206\u3001\u307e\u305f\u306fBochner\u306e\u7a4d\u5206\u3002\u6982\u5ff5\u306e\u540d\u524d\u306f\u3001\u6570\u5b66\u8005I. M. Gelfanda\u3068B.J.\u306e\u540d\u524d\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059\u3002\u30da\u30c6\u30a3\u30b5\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3055\u305b\u3066 \uff08 \u304a\u304a \u3001 a \u3001 m \uff09\uff09 {displaystyle\uff08omega\u3001{mathcal {a}}\u3001mu\uff09} \u305d\u308c\u306f\u5c3a\u5ea6\u306e\u5c3a\u5ea6\u306b\u306a\u308a\u3001 \u30d0\u30c4 {displaystyle x} \u305d\u308c\u306f\u3001\u81ea\u660e\u3067\u306a\u3044\u30ab\u30c3\u30d7\u30eb\u7a7a\u9593\u3092\u5099\u3048\u305f\u7dda\u5f62\u30c8\u30d4\u30ab\u30eb\u7a7a\u9593\u306b\u306a\u308a\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 \u2217 \u3002 {displaystyle x^{*}\u3002} \u95a2\u6570\u306b\u3064\u3044\u3066 f \uff1a \u304a\u304a \u2192 \u30d0\u30c4 {displaystyle fcolon omega\u304b\u3089x} \u305d\u3046\u3060\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059 \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u7d71\u5408\u53ef\u80fd \u5404\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u5834\u5408 a \u2208 a {displaystyle ain {mathcal {a}}} \u3059\u3079\u3066\u306e\u6a5f\u80fd \u30d0\u30c4 \u2217 \u2208 \u30d0\u30c4 \u2217 {displaystyle x^{*} in x^{*}}} \u305d\u306e\u3088\u3046\u306a\u8981\u7d20\u304c\u3042\u308a\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 a {displaystyle x_ {a}} \u7a7a \u30d0\u30c4 \u3001 {displaystyle x\u3001} \u305d\u308c\u304b \u27e8 \u30d0\u30c4 \u2217\u3001 \u30d0\u30c4 A\u27e9 = \u222b A\u27e8 \u30d0\u30c4 \u2217\u3001 f \uff08 t \uff09\uff09 \u27e9 m \uff08 dt \uff09\uff09 \u3002 {displaystyle langle x^{*}\u3001x_ {a} rangle = int _ {a} langle x^{*}\u3001f\uff08t\uff09rangle mu\uff08{mbox {d}}\u3001t\uff09\u3002}} \u70b9 \u30d0\u30c4 a \u3001 {displaystyle x_ {a}\u3001} \u4e0a\u8a18\u306e\u30d1\u30bf\u30fc\u30f3\u3067\u306f\u3001\u547c\u3070\u308c\u307e\u3059 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206 \u95a2\u6570\u304b\u3089 f {displaystyle f} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306b a {displaystyle a} \u6e2c\u5b9a\u306b\u5bfe\u3057\u3066 m {displaystyle mu} \u30b7\u30f3\u30dc\u30eb\u3067\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059 \u30d0\u30c4 A= \uff08 p \uff09\uff09 \u222b Af dm \u3002 {displaystyle x_ {a} =\uff08p\uff09int _ {a} f {mbox {d}} mu\u3002} \u5404\u95a2\u6570 f {displaystyle f} \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u7d71\u5408\u53ef\u80fd\u306a\u6e2c\u5b9a\u3082\u4e0d\u5341\u5206\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u8ab0\u306b\u3068\u3063\u3066\u3082 \u30d0\u30c4 \u2217 \u2208 \u30d0\u30c4 \u2217 {displaystyle x^{*} in x^{*}}} \u95a2\u6570 \u30d0\u30c4 \u2217\u2218 f {displaystyle x^{*} circ f} \u30b9\u30ab\u30e9\u30fc\u306e\u672c\u4f53\u3067\u6e2c\u5b9a\u53ef\u80fd\u3067\u3059\u3002 \u3082\u3057\u3082 \u30d0\u30c4 {displaystyle x} \u30d0\u30ca\u30c3\u30cf\u306e\u7a7a\u9593\u3001\u6a5f\u80fd\u3067\u3059 A\u220b a \u21a6 \uff08 p \uff09\uff09 \u222b Af dm m\u3053\u306eylepent Yatine Patiney Male Foys Supe\uff08Fri\uff09Malm Male Mjoy Mjoy Mjoy Mjoy Mjoy Mjoy Mjoy Mjoy Cheme\u306b\u3064\u3044\u3066\u8a71\u3057\u5408\u3046 \u547c\u3070\u308c\u308b\u5305\u62ec\u7684\u306a\u5305\u62ec\u7684\u306a\u30d9\u30af\u30bf\u30fc\u3067\u3059 \u30de\u30fc\u30af\u306e\u306a\u3044\u30da\u30c6\u30a3\u30b9 \u95a2\u6570\u304b\u3089 f \u3002 {displaystyle f\u3002}  \u53cd\u5c04\u7a7a\u9593\u306b\u5024\u3092\u6301\u3064\u6a5f\u80fd\u306e\u5834\u5408\u3001\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3068\u30c0\u30f3\u30d5\u30a9\u30fc\u30c9\u306e\u610f\u5473\u3067\u7d61\u307f\u5408\u3063\u305f\u6982\u5ff5\u304c\u4e00\u81f4\u3057\u307e\u3059\u3002 \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u5b8c\u5168\u306a\u6a5f\u80fd\u306e\u4f8b\u3002\u305d\u306e\u6a19\u6e96\u304c\u7d71\u5408\u3067\u304d\u306a\u3044\u3002  \u3055\u305b\u3066 \u30d0\u30c4 {displaystyle x} \u30d2\u30eb\u30d9\u30eb\u30c8\u306e\u30b9\u30da\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059 { \u305d\u3046\u3067\u3059 n \uff1a n \u2208 n } {displaystyle {e_ {n}\u30b3\u30ed\u30f3\u3001nin mathbb {n}}} \u3053\u308c\u306f\u3001\u3053\u306e\u7a7a\u9593\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u30aa\u30eb\u30bd\u30fc\u30de\u30eb\u30dd\u30a4\u30f3\u30c8\u306b\u306a\u308a\u307e\u3059\u3002\u95a2\u6570 f \uff1a [ 0 \u3001 \u221e \uff09\uff09 \u2192 \u30d0\u30c4 {displaystyle fcolon [0\u3001infty\uff09\u304b\u3089x} \u4e0e\u3048\u3089\u308c\u305f\u30d1\u30bf\u30fc\u30f3 f \uff08 t \uff09\uff09 = 1n\u305d\u3046\u3067\u3059 n\u3001 t \u2208 [ n \u3001 n + \u521d\u3081 \uff09\uff09 \u3001 n \u2208 n Clegles\u306eMM\u5974\u96b7\uff09\uff09M 1 Mafines Mjoy\u3001Kubate\u3001Mmbm MM MMM HMMQu\u00e1mM\u00e1memem\u00f6tubkmb\uff09mmm mmb\uff09 \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306f\u3001\u30ec\u30d9\u30fc\u30bc\u306e\u6e2c\u5b9a\u306b\u6fc0\u3057\u3044\u3067\u3059\u304c\u3001 \u222b 0\u221e\u2016 f \uff08 t \uff09\uff09 \u2016 d t = \u221e \u3002 {displaystyle int _ {0}^{infty} | f\uff08t\uff09| dt = infty\u3002}} \u4e0d\u5b8c\u5168\u306a\u95a2\u6570\u306e\u4f8b  \u95a2\u6570 f \uff1a [ 0 \u3001 \u521d\u3081 ] \u2192 c 0 \u3001 {displaystyle fcolon [0,1]\u304b\u3089c_ {0}\u3001} \u4e0e\u3048\u3089\u308c\u305f\u30d1\u30bf\u30fc\u30f3 f \uff08 t \uff09\uff09 = (n\u22c51(0,1n](t))n\u2208N{displaystyle f\uff08t\uff09= left\uff08ncdot mathbf {1} _ {\uff080\u3001{tfrac {1} {n}}]}\uff08t\uff09_ {nin mathbb {n}}}} \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306f\u7d71\u5408\u3067\u304d\u307e\u305b\u3093\u3002\u78ba\u304b\u306b\u3001\u3055\u305b\u3066\u304f\u3060\u3055\u3044 \u30d0\u30c4 \u2217 \u2208 c 0 \u2217 {displaystyle x^{*} in c_ {0}^{*}} \u3068\u3055\u305b\u3066\u304f\u3060\u3055\u3044 \u3068 = \uff08 t n \uff09\uff09 n \u2208 N{displaystyle y =\uff08t_ {n}\uff09_ {nin mathbb {n}}}} \u7a7a\u9593\u304b\u3089\u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u306b\u306a\u308a\u307e\u3059 \u2113 \u521d\u3081 {displaystyle ell ^{1}} \uff08\u30b9\u30da\u30fc\u30b9\u306e\u8acb\u6c42\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 c 0 {displaystyle c_ {0}} \uff09\u3002 \u222b 01| \u30d0\u30c4 \u2217f \uff08 t \uff09\uff09 | d t = \u222b 01| \u2211n=1\u221etnn1(0,1n](t)| d t \u2a7d \u222b 01\u2211 n=1\u221e| t n| n 1(0,1n]\uff08 t \uff09\uff09 d t = \u2211 n=1\u221e| t n| n de 1n= \u2211 n=1\u221e| t n| < \u221e \u3002 {displaystyle int _ {0}^{1} | x^{*} f\uff08t\uff09| dt = int _ {0}^{1} left | sum _ {n = 1}^{infty} lant int _ {0}^{1} sum _ {n = 1}^{infty} | t_ {n} | nmathbf {1} _ {\uff080\u3001{tfrac {1} {n}}]}}\uff08t\uff09\u3001dt = sum _ {n = 1} {nc} {nc} {nc} } {n}} = sum _ {n = 1}^{infty} | t_ {n} | N\u2208 c 0 \u3001 {displaystyle\uff08p\uff09int _ {0}^{1} f\uff08t\uff09\u3001dt =\uff08x_ {n}\uff09_ {nin mathbb {n}} in c_ {0}\u3001} \u306b \u30d0\u30c4 n= \u222b 01\u30d0\u30c4 n\u2217f \uff08 t \uff09\uff09 d t = \u222b 01n de 1(0,1n]\uff08 t \uff09\uff09 d t = \u521d\u3081 \u3001 n \u2208 n \u3001 {displaystyle x_ {n} = int _ {0}^{1} x_ {n}^{*} f\uff08t\uff09\u3001dt = int _ {0}^{1} ncdot mathbf {1} _ {\uff080\u3001{tfrac {1} {n} {n}} {n}\uff09 } \u3069\u3053 \u30d0\u30c4 n \u2217 \u2208 c 0 \u2217 {displaystyle x_ {n}^{*} in c_ {0}^{*}} \u7a7a\u9593\u306e\u8981\u7d20\u3092\u5272\u308a\u5f53\u3066\u307e\u3059 c 0 {displaystyle c_ {0}} \u5f7c\u306e n {displaystyle n}  &#8211; \u3042\u306a\u305f\u306e\u8a00\u8449\u3002 \u3055\u305b\u3066 m {displaystyle mu} \u30b9\u30da\u30fc\u30b9\u306e\u5c3a\u5ea6\u306b\u306a\u308a\u307e\u3059 \u304a\u304a \u3002 {displaystyle omega\u3002} \u30d0\u30ca\u30c3\u30cf\u306e\u30b9\u30da\u30fc\u30b9\u304c\u6240\u6709\u3055\u308c\u3066\u3044\u308b\u3068\u8a00\u3044\u307e\u3059 m {displaystyle mu} -pip\uff08 Pettis Integral\u30d7\u30ed\u30d1\u30c6\u30a3 \uff09\u3001\u5404\u8ca7\u5f31\u306a\u6e2c\u5b9a\u53ef\u80fd\u306a\u95a2\u6570\u3068 m {displaystyle mu} -W.W.\u9650\u3089\u308c\u3066\u3044\u306a\u3044 f \uff1a \u304a\u304a \u2192 \u30d0\u30c4 {displaystyle fcolon omega\u304b\u3089x} \u305d\u308c\u306f\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u6fc0\u3057\u3044\u3067\u3059 m \u3002 {displaystyle mu\u3002} \u7279\u306b\u3001\u30eb\u30d9\u30fc\u30b0\u30fb\u30d1\u30a4\u30d7\u306f\u3001\u30e6\u30cb\u30c3\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u30eb\u30d9\u30fc\u30b0\u306e\u6e2c\u5b9a\u306e\u5834\u5408\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u30d0\u30ca\u30c3\u30cf\u306e\u30b9\u30da\u30fc\u30b9\u306f\u3001\u5f7c\u304c\u6240\u6709\u6a29\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u304d\u306bPIP\u304c\u6240\u6709\u3057\u3066\u3044\u308b\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059 m {displaystyle mu}  &#8211; \u5b8c\u6210\u306e\u5404\u6e2c\u5b9a\u306e\u30d1\u30a4\u30d7 m \u3002 {displaystyle mu\u3002}  \u3059\u3079\u3066\u306e\u30d0\u30ca\u30c3\u30cf\u30b9\u30da\u30fc\u30b9\u304cPIP\u304c\u6240\u6709\u3057\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305f\u3068\u3048\u3070\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u7a7a\u9593\u3067\u6307\u5b9a\u3055\u308c\u305f\u9023\u7d9a\u95a2\u6570\u306e\u7a7a\u9593 \u304a\u304a \u521d\u3081 + \u521d\u3081 = [ 0 \u3001 \u304a\u304a \u521d\u3081 ] \u3001 {displaystyle omega _ {1}+1 = [0\u3001omega _ {1}]\u3001} \u3069\u3053 \u304a\u304a \u521d\u3081 {displaystyle omega _ {1}} \u6700\u521d\u306e\u4e92\u63db\u6027\u306e\u306a\u3044\u6ce8\u6587\u756a\u53f7\u3092\u610f\u5473\u3057\u307e\u3059\u3001\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u3042\u308a\u307e\u305b\u3093 m {displaystyle mu}  &#8211; \u8ca7\u5f31\u306a\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u610f\u5473\u3067Baire\u3092\u6240\u6709\u3057\u3066\u3044\u308b\u30b5\u30d6\u30bb\u30c3\u30c8\u306e\u03c3\u914d\u7bc0\u306e\u6e2c\u5b9a\u5024\u3092\u64ae\u5f71\u3059\u308b [\u521d\u3081] \u3002\u30b9\u30da\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 {displaystyle x} \uff08\u4f8b\u3048\u3070\u3002 \u30b8\u30a7\u30fc\u30e0\u30ba\u306e\u9577\u3044\u30b9\u30da\u30fc\u30b9 \uff09 \u305d\u306e\u3088\u3046\u306a \u30d0\u30c4 {displaystyle x} \u79c1 \u30d0\u30c4 \u2217 {displaystyle x^{*}} \u5f7c\u3089\u306f\u30e9\u30c9\u30f3\u30fb\u30cb\u30b3\u30c7\u30a3\u30de\uff08RNP\uff09\u306e\u8ca1\u7523\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u304c\u3001\u5f7c\u3089\u81ea\u8eab\u306fPIP\u306e\u7279\u6027\u3092\u6301\u3063\u3066\u3044\u307e\u305b\u3093 [2] \u3002\u9023\u7d9a\u6027\u4eee\u8aac\uff08CH\uff09\u307e\u305f\u306f\u5426\u5b9a\u3068\u516c\u7406\u30de\u30fc\u30c6\u30a3\u30f3\u306e\u4eee\u5b9a\u306e\u4e0b\u3067\u3001\u30b8\u30a7\u30fc\u30e0\u30ba\u306e\u9577\u3044\u7a7a\u9593\u306b\u306f\u30eb\u30d9\u30fc\u30b0\u30d1\u30c3\u30d7\u306e\u8ca1\u7523\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u306e\u7d71\u5408\u53ef\u80fd\u306a\u6a5f\u80fd\u306e\u7a7a\u9593 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3055\u305b\u3066 \uff08 \u304a\u304a \u3001 a \u3001 m \uff09\uff09 {displaystyle\uff08omega\u3001{mathcal {a}}\u3001mu\uff09} \u6709\u9650\u306e\u6e2c\u5b9a\u5024\u3092\u5099\u3048\u305f\u30b9\u30da\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u30d0\u30ca\u30c3\u30cf\u306e\u30b9\u30da\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059\u3002\u5b87\u5b99\u3067 p \uff08 m \u3001 \u30d0\u30c4 \uff09\uff09 {displaystyle {mathcal {p}}\uff08mu\u3001x\uff09} \u3059\u3079\u3066\u306e\u95a2\u6570\uff08\u540c\u7b49\u306e\u30af\u30e9\u30b9 m {displaystyle mu} -P.W.\uff09\u30da\u30c6\u30a3\u30b9\u306e\u610f\u5473\u3067\u7d71\u5408\u53ef\u80fd f \uff1a \u304a\u304a \u2192 \u30d0\u30c4 \u3001 {displaystyle fcolon omega\u304b\u3089x\u3001} \u7279\u5b9a\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u6a5f\u80fd\u3055\u305b\u307e\u3057\u305f \u2016 f \u2016 = \u3059\u3059\u308b { \u222b\u03a9|x\u2217f(t)|\u03bc(dt):x\u2217\u2208X\u2217,\u2016x\u2217\u2016\u2a7d1} {displaystyle | f | = sup\u5de6{int _ {omega} | x^{*} f\uff08t\uff09|\u3001mu\uff08dt\uff09\u30b3\u30ed\u30f3\u3001x^{*} ,, | x^{*} | leqslant 1right}}}} \u6a19\u6e96\u3067\u3059\u3002\u5b9a\u7fa9\u304b\u3089\u76f4\u63a5\u306f\u3001\u305d\u306e\u5834\u5408\u3092\u793a\u3057\u3066\u3044\u307e\u3059 f \u2208 p \uff08 m \u3001 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle fin {mathcal {p}}\uff08mu\u3001x\uff09\u3001} \u306b \u2016 (P)\u222b\u03a9fd\u03bc\u2016 \u2a7d \u2016 f \u2016 \u3002 {displaystyle\u5de6|\uff08p\uff09int _ {omega} f\u3001dmu\u53f3| leqslant | f |\u3002} \u3082\u3057\u3082 \u30d0\u30c4 {displaystyle x} \u7121\u9650\u306e\u5bf8\u6cd5\u7a7a\u9593\u3067\u3059 p \uff08 m \u3001 \u30d0\u30c4 \uff09\uff09 {displaystyle {mathcal {p}}\uff08mu\u3001x\uff09} \u5b8c\u5168\u306a\u30b9\u30da\u30fc\u30b9\uff08\u30d0\u30ca\u30c3\u30cf\u30b9\u30da\u30fc\u30b9\uff09\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30d0\u30ec\u30eb\u30b9\u30da\u30fc\u30b9\u3067\u3059 [6] \uff08\u3057\u305f\u304c\u3063\u3066\u3001Banach-Steinhaus\u306e\u3044\u304f\u3064\u304b\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3068\u9589\u3058\u305f\u30c1\u30e3\u30fc\u30c8\u306b\u95a2\u3059\u308b\u4e3b\u5f35\u306f\u3001\u305d\u308c\u306b\u95a2\u9023\u3057\u3066\u771f\u5b9f\u3067\u3059\uff09\u3002 \u2191  G.A.\u30a8\u30c9\u30ac\u30fc\u3001 \u30d0\u30ca\u30c3\u30cf\u7a7a\u9593\u3067\u306e\u6e2c\u5b9a\u53ef\u80fd\u6027i \u3001\u30a4\u30f3\u30c7\u30a3\u30a2\u30ca\u5927\u5b66\u7b97\u6570\u3002 J.\u300126\uff081977\uff09\u3001s\u3002 663\u2013667\u3002  \u2191  G.A.\u30a8\u30c9\u30ac\u30fc\u3001 \u9577\u3044\u30b8\u30a7\u30fc\u30e0\u30ba\u30b9\u30da\u30fc\u30b9 \u3001\u6e2c\u5b9a\u7406\u8ad6\u306b\u95a2\u3059\u308b\u4f1a\u8b70\u306e\u8b70\u4e8b\u9332\u3001\u6570\u5b66\u306e\u8b1b\u7fa9\u30ce\u30fc\u30c8\u3001Vol\u3002 794\u3001\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af\u30011980\u5e74\u3002  \u2191  D.H. Fremlin\u3001M\u3002Talagrand\u3001 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206\u3068\u30a8\u30eb\u30b4\u30fc\u30c9\u306e\u624b\u6bb5\u3078\u306e\u9069\u7528\u3092\u5099\u3048\u305f\u52a0\u6cd5\u30bb\u30c3\u30c8\u30d5\u30a1\u30f3\u30af\u30b7\u30e7\u30f3\u306e\u5206\u89e3\u5b9a\u7406 \u3001 \u7b97\u6570\u3002 Z.\u3001168\uff081979\uff09\u3001s\u3002 117\u2013142\u3002  \u2191  R.\u30d5\u30e9\u30f3\u30af\u30f4\u30a3\u30c3\u30c1\u3001G\u3002Plebanek\u3001 \u4ee3\u6570\u3068\u6a5f\u80fd\u306e\u6e2c\u5b9a\u5024\u306e\u30a2\u30af\u30bb\u30b9\u4e0d\u53ef\u80fd\u306a\u30d5\u30a3\u30eb\u30bf\u30fc \u306e\u4e0a L\u221e(\u03bb)\u2217.{displaystyle l^{infty}\uff08lambda\uff09^{*}\u3002} Studia Math\u3002 108\uff081994\uff09\u3001s\u3002 191\u2013200\u3002  \u2191  G.A.\u30a8\u30c9\u30ac\u30fc\u3001 \u30d0\u30ca\u30c3\u30cf\u7a7a\u9593\u3067\u306e\u6e2c\u5b9a\u53ef\u80fd\u6027II \u3001\u30a4\u30f3\u30c7\u30a3\u30a2\u30ca\u5927\u5b66\u7b97\u6570\u3002 J.\u300128\uff081979\uff09\u3001s\u3002 559\u2013579\u3002  \u2191  L. Drewnowski\u3001M\u3002Florencio\u3001P.J\u3002\u30d1\u30a6\u30eb\u3001 Pettis\u7d71\u5408\u6a5f\u80fd\u306e\u7a7a\u9593\u306f\u30d0\u30ec\u30eb\u3055\u308c\u3066\u3044\u307e\u3059 \u3001Proc\u3002 Amer\u3002\u7b97\u6570\u3002 Soc\u3002 114\uff081992\uff09\u3001s\u3002 687\u2013694\u3002  J.K.\u30d6\u30eb\u30c3\u30af\u30b9\u3001 \u30d0\u30ca\u30c3\u30cf\u7a7a\u9593\u306b\u304a\u3051\u308b\u5f31\u304f\u3066\u5f37\u3044\u7a4d\u5206\u306e\u8868\u73fe \u3001Proc\u3002\u30ca\u30c3\u30c8\u3002\u30a2\u30ab\u30c7\u30df\u30fc\u3002 SCI\u3002 U.S.A. 63\u30011969\u3001266\u2013270\u3002 \u5168\u6587 J.\u30c7\u30a3\u30b9\u30c6\u30eb\u3001J.J\u3002 UHL\uff1a \u30d9\u30af\u30c8\u30eb\u6e2c\u5b9a \u3002\u30d7\u30ed\u30d3\u30c7\u30f3\u30b9\u3001\u30ed\u30fc\u30c9\u30a2\u30a4\u30e9\u30f3\u30c9\uff1a\u30a2\u30e1\u30ea\u30ab\u6570\u5b66\u5354\u4f1a\u30011977\u5e74 I. M.\u30b2\u30eb\u30d5\u30a1\u30f3\u30c9\u3001 \u7dda\u5f62\u7a7a\u9593\u7406\u8ad6\u306e\u88dc\u984c\u306b\u3064\u3044\u3066 \u3001 \u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u3002\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3002 SCI\u3002\u7b97\u6570\u3002\u305d\u308c\u306f\u30e1\u30ab\u30f3\u3001\u5927\u5b66Kharkoff it soc\u3002\u7b97\u6570\u3002 Kharkoff\u3001iv\u3002 ser\u3002 13\u30011936\u300135-40 LDL 0014.16202 K.\u30df\u30e5\u30fc\u30b8\u30e3\u30eb\u3001 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206\u306e\u7406\u8ad6\u306e\u30c8\u30d4\u30c3\u30af \u3001\u30c8\u30ea\u30a8\u30b9\u30c6\u5927\u5b66\u6570\u5b66\u7814\u7a76\u6240\u306e\u5831\u544a\u3001xxiii\uff081991\uff09\u3001177-262 K.\u30df\u30e5\u30fc\u30b8\u30e3\u30eb\u3001 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206 \u3001\u30e1\u30b8\u30e3\u30fc\u7406\u8ad6I\u3001\u30ce\u30fc\u30b9\u30db\u30e9\u30f3\u30c92002\u3001531-586\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af M.\u30bf\u30e9\u30b0\u30e9\u30f3\u30c9\u3001 \u30da\u30c6\u30a3\u30b9\u7a4d\u5206\u304a\u3088\u3073\u6e2c\u5b9a\u7406\u8ad6 \u3001AMS\u3044\u3044\u3048\u306e\u56de\u9867\u9332307\uff081984\uff09       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/16030#breadcrumbitem","name":"Pettis Integral -Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178"}}]}]