[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13378#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13378","headline":"\u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u30b5\u30c3\u30c4 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u30b5\u30c3\u30c4 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u6587 Stefan Banach\u3068Stanis\u0142awMazur\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f1933\u5e74\u304b\u3089\u3001\u6a5f\u80fd\u5206\u6790\u306e\u30b5\u30d6\u30a8\u30ea\u30a2\u304b\u3089\u306e\u53e4\u5178\u7684\u306a\u6587\u3067\u3059\u3002\u4ed6\u306e\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u30b3\u30d4\u30fc\u3092\u542b\u3080\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u4e2d\u306b\u306f\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} after-content-x4 \u5b9a\u6570\u95a2\u6570 [ 0 \u3001 \u521d\u3081","datePublished":"2019-03-16","dateModified":"2019-03-16","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/44211c4c325ea7edb9462e7ccecda09841a41216","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/44211c4c325ea7edb9462e7ccecda09841a41216","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13378","wordCount":5570,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u6587 Stefan Banach\u3068Stanis\u0142awMazur\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f1933\u5e74\u304b\u3089\u3001\u6a5f\u80fd\u5206\u6790\u306e\u30b5\u30d6\u30a8\u30ea\u30a2\u304b\u3089\u306e\u53e4\u5178\u7684\u306a\u6587\u3067\u3059\u3002\u4ed6\u306e\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u30b3\u30d4\u30fc\u3092\u542b\u3080\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u4e2d\u306b\u306f\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5b9a\u6570\u95a2\u6570 [ 0 \u3001 \u521d\u3081 ] \u2192 R{displaystyle [0,1] rightArrow {mathbb {r}}} Supremums Standard\u304c1\u3064\u3067\u3059 \u30e6\u30cb\u30d0\u30fc\u30b5\u30eb \u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u3002 \u306f        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k {displaystyle k} \u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b9\u30da\u30fc\u30b9\u3001\u3053\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u793a\u3059\u304b\u3067\u3059 c \uff08 k \uff09\uff09 {displaystyle c\uff08k\uff09} \u306e\u4e00\u5b9a\u306e\u6a5f\u80fd\u306e\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0 k {displaystyle k} \u5f8c r {displaystyle mathbb {r}} Supremums Standard\u3067        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u2016 de \u2016 \u221e{displaystyle | cdot | _ {infty}} \u3002 \u6700\u521d\u306e\u30d0\u30fc\u30b8\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] Banach-Mazur\u6587\u306e\u6700\u521d\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3067 k {displaystyle k} Cantor\u306e\u4e0d\u9023\u7d9a d {displaystyledelta} \uff1a \u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u3054\u3068\u306b \u3068 {displaystyle e} \u306e\u7b49\u5c3a\u6027\u7dda\u5f62\u6f14\u7b97\u5b50\u306f\u3042\u308a\u307e\u3059\u304b \u3068 {displaystyle e} \u5f8c c \uff08 d \uff09\uff09 {displaystyle c\uff08delta\uff09} \u3002 \u6b21\u306e\u8a3c\u62e0\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u30a2\u30a4\u30bd\u30e1\u30c8\u30ea\u3092\u3069\u306e\u3088\u3046\u306b\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u3046\u3067\u3059 \u3068 1‘ {displaystyle e_ {1} ‘} \u306e\u30c7\u30e5\u30a2\u30eb\u30b9\u30da\u30fc\u30b9\u306e\u5747\u4e00\u306a\u30dc\u30fc\u30eb \u3068 {displaystyle e} \u3002 Banach-Alaoglu\u306e\u30d5\u30ec\u30fc\u30ba\u306b\u3088\u308b\u3068\u3001\u3053\u308c\u306f\u5f31\u3044*\u30c8\u30dd\u30ed\u30b8\u30fc\u306b\u95a2\u3057\u3066\u3001\u305d\u3057\u3066\u5206\u96e2\u6027\u306e\u305f\u3081\u306b\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u30e1\u30c8\u30ea\u30c3\u30af\u30b9\u3055\u3048\u3059\u308b\u3053\u3068\u3055\u3048\u3042\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u5b89\u5b9a\u3057\u305f\u3001\u526f\u691c\u67fb\u306e\u56f3\u304c\u3042\u308a\u307e\u3059 \u03d5 \uff1a d \u2192 \u3068 1‘ {displaystylephi\u30b3\u30ed\u30f3\u30c7\u30eb\u30bfRightArrow E_ {1} ‘} \u3001\u30c8\u30dd\u30ed\u30b8\u306e\u7d50\u679c\u306b\u3088\u308c\u3070\u3001\u3059\u3079\u3066\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30e1\u30c8\u30ea\u30b9\u53ef\u80fd\u306a\u7a7a\u9593\u306f\u3001\u30ab\u30f3\u30bf\u30fc\u306e\u4e0d\u9023\u7d9a\u306e\u5b89\u5b9a\u3057\u305f\u7d75\u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002\u3042\u306a\u305f\u306f\u4eca\u5b9a\u7fa9\u3057\u307e\u3059 t \uff1a \u3068 \u2192 c \uff08 d \uff09\uff09 {displaystyle tcolon erightarrow c\uff08delta\uff09} \u7d42\u3048\u305f \uff08 t \u30d0\u30c4 \uff09\uff09 \uff08 d \uff09\uff09 \uff1a= \uff08 \u03d5 \uff08 d \uff09\uff09 \uff09\uff09 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001  \u30d0\u30c4 \u2208 \u3068 \u3001  d \u2208 d {displaystyle\uff08TX\uff09\uff08delta\uff09\uff1a=\uff08phi\uff08delta\uff09\uff09\uff08x\uff09\u3001e\u3001delta in delta} \u3001\u305d\u3046\u3067\u3059 t {displaystylet} \u3069\u3046\u3084\u3089\u7dda\u5f62\u3068\u305d\u306e\u305f\u3081 \u2016 t \u30d0\u30c4 \u2016\u221e\uff1a= sup\u03b4\u2208\u0394|\uff08 t \u30d0\u30c4 \uff09\uff09 \uff08 d \uff09\uff09 |= sup\u03b4\u2208\u0394|\u03d5 \uff08 d \uff09\uff09 \uff08 \u30d0\u30c4 \uff09\uff09 |= supf\u2208E1\u2032|f \uff08 \u30d0\u30c4 \uff09\uff09 |= \u2016 \u30d0\u30c4 \u2016 {displaystyle | tx | _ {infty}\uff1a= sup _ {delta in delta} |\uff08tx\uff09\uff08delta\uff09| = sup _ {delta in delta} | phi\uff08delta\uff09\uff08x\uff09| = sup _ {fin e_ {1} ‘} | f\uff08x\uff09| = | x |} \u307e\u305f\u3001\u7b49\u5c3a\u6027\u3001\u305d\u308c\u306b\u3088\u308a\u3001\u30cf\u30fc\u30f3\u30d0\u30ca\u30c3\u30cf\u904b\u52d5\u304b\u3089\u306e\u6700\u5f8c\u306e\u5e73\u7b49\u304c\u7d9a\u304d\u3001\u306e\u526f\u7523\u6027\u304b\u3089\u306e\u6700\u5f8c\u304b\u30892\u756a\u76ee\u306e\u5e73\u7b49\u304c\u7d9a\u304d\u307e\u3059 \u03d5 {displaystyle phi\u3001} \u3002 2\u756a\u76ee\u306e\u30d0\u30fc\u30b8\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6b21\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u306f\u7d50\u8ad6\u3068\u3057\u3066\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002 \u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u3054\u3068\u306b \u3068 {displaystyle e} \u306e\u7b49\u5c3a\u6027\u3001\u7dda\u5f62\u6f14\u7b97\u5b50\u306f\u3042\u308a\u307e\u3059\u304b \u3068 {displaystyle e} \u5f8c c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u3002 \u305d\u308c\u305e\u308c\u306b f \u2208 c \uff08 d \uff09\uff09 {displaystyle fin c\uff08delta\uff09} \u3042\u306a\u305f\u306f\u5b9a\u7fa9\u3057\u307e\u3059 f~\uff1a [ 0 \u3001 \u521d\u3081 ] \u2192 r {displaystyle {tilde {f}} colon [0,1] rightArrow mathbb {r}} \u30aa\u30f3\u306e\u4e00\u5b9a\u306e\u95a2\u6570\u3068\u3057\u3066 d {displaystyledelta} \u3068 f {displaystyle f} \u4e00\u81f4\u3057\u3066\u9593\u9694\u3067 [ 0 \u3001 \u521d\u3081 ] \u2216 d {displaystyle [0,1] setminus delta} \u7dda\u5f62\u3067\u3059\u3002\u30a4\u30e9\u30b9\u30c8 f \u21a6 f~{displaystyle fmapsto {tilde {f}}} \u6b21\u306b\u3001\u7b49\u5c3a\u6027\u57cb\u3081\u8fbc\u307f\u3092\u5b9a\u7fa9\u3057\u307e\u3059 c \uff08 d \uff09\uff09 {displaystyle c\uff08delta\uff09} \u5f8c c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u305d\u3057\u3066\u3001\u30a2\u30b5\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u6587\u306e\u6700\u521d\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u304b\u3089\u7d9a\u304d\u307e\u3059\u3002 \u305d\u308c\u3068\u4e00\u7dd2\u306b c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u9707\u3048\u30d9\u30fc\u30b9\u304c\u3042\u308a\u3001\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306b\u57fa\u672c\u7684\u306a\u7d50\u679c\u306e\u7406\u8ad6\u306b\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u306f\u3001\u4ee5\u4e0b\u306e\u30c6\u30ea\u30fcJ.\u30e2\u30ea\u30bd\u30f3\u306e\u672c\u306b\u3042\u308a\u307e\u3059\u3002 \u8eab\u9707\u3044\u57fa\u5730\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u8ca1\u7523\u306f\u3001\u5f53\u4e8b\u8005\u3092\u7d99\u627f\u3057\u307e\u305b\u3093\u3002 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u9707\u3048\u30d9\u30fc\u30b9\u304c\u3042\u308a\u3001\u9707\u3048\u30d9\u30fc\u30b9\u306e\u306a\u3044\u5206\u96e2\u53ef\u80fd\u306a\u7acb\u65b9\u4f53\u304c\u3042\u308a\u3001\u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u30d5\u30ec\u30fc\u30ba\u306b\u3088\u308b\u3068\u3001 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u53d7\u3051\u53d6\u308b\u3002\u540c\u3058\u7406\u7531\u3067\u3001\u8fd1\u4f3c\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u90e8\u5206\u5ba4\u3092\u7d99\u627f\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u30d0\u30ca\u30c3\u30cf\u30fb\u30de\u30ba\u30fc\u30eb\u306e\u6587\u306e\u5185\u5bb9\u3067\u3042\u308b\u3059\u3079\u3066\u306e\u5206\u96e2\u53ef\u80fd\u306a\u7acb\u65b9\u4f53\u306e\u30af\u30e9\u30b9\u306b\u304a\u3051\u308b\u5730\u4e0b\u5c64\u306b\u95a2\u3059\u308b\u666e\u904d\u7684\u306a\u5206\u96e2\u53ef\u80fd\u306a\u90e8\u5c4b\u3067\u3059\u3002\u5546\u306e\u5f62\u6210\u306e\u89b3\u70b9\u304b\u3089\u3082\u666e\u904d\u7684\u306a\u5206\u96e2\u53ef\u80fd\u306a\u7acb\u65b9\u4f53\u3082\u3042\u308a\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u7b49\u5c3a\u6027\u540c\u578b\u304c\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u5546\u3068\u898b\u3048\u308b\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u21131{displaystyle ell ^{1}} \u306f\u3002 AleksanderPe\u0142czy\u0144ski\u306f1962\u5e74\u306b\u3001\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u306e\u90e8\u5c4b\u306b\u95a2\u3059\u308b\u6b21\u306e\u58f0\u660e\u3092\u793a\u3057\u307e\u3057\u305f \u3068 {displaystyle e} \u540c\u7b49\u3067\u3059\uff1a \u3068 {displaystyle e} \u5730\u4e0b\u5c64\u306b\u95a2\u3059\u308b\u666e\u904d\u7684\u306a\u5206\u96e2\u53ef\u80fd\u306a\u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u3067\u3059\u3002 \u3068 {displaystyle e} 1\u3064\u3082\u542b\u307e\u308c\u3066\u3044\u307e\u3059 c \uff08 d \uff09\uff09 {displaystyle c\uff08delta\uff09} \u540c\u578b\u5730\u4e0b\u7b49\u5c3a\u6027\u3002 \u3068 {displaystyle e} 1\u3064\u3082\u542b\u307e\u308c\u3066\u3044\u307e\u3059 c \uff08 [ 0 \u3001 \u521d\u3081 ] \uff09\uff09 {displaystyle c\uff08[0,1]\uff09} \u540c\u578b\u5730\u4e0b\u7b49\u5c3a\u6027\u3002 \u8981\u7d20\u304c\u3042\u308a\u307e\u3059 xn,k\u2208 \u3068 {displaystyle x_ {n\u3001k} in e} \u305f\u3081\u306b n \u2208 N{displaystyle nin mathbb {n}} \u3068 k = 0 \u3001 \u521d\u3081 \u3001 … 2n –  \u521d\u3081 {displaystyle k = 0,1\u3001ldots 2^{n} -1} \u3001 \u3068\u306a\u308b\u3053\u3068\u306b\u3088\u3063\u3066 xn,k= xn+1,2k+ xn+1,2k+1{displaystyle x_ {n\u3001k}\u3001=\u3001x_ {n+1.2k}+x_ {n+1.2k+1}}}} \u3068 \u2016\u2211k=02n\u22121tkxn,k\u2016= maxk=0,\u20262n\u22121|tk|{displaystyle\u5de6| sum _ {k = 0}^{2^{n} -1} t_ {k} x_ {n\u3001k}\u53f3| = max _ {k = 0\u3001ldots 2^{n} -1}\u5de6| t_ {k}\u53f3|}} \u3059\u3079\u3066\u306e\u30b9\u30ab\u30e9\u30fc\u7528 tk\u2208 R{displaystyle t_ {k} in mathbb {r}} \u9069\u7528\u53ef\u80fd\u3067\u3059\u3002 S.\u30d0\u30ca\u30c3\u30cf\u3001S\u3002\u30de\u30ba\u30fc\u30eb\uff1a \u7dda\u5f62\u5bf8\u6cd5\u306e\u7406\u8ad6\u306b\u3064\u3044\u3066 \u3001Studia Mathematica\uff081933\uff09\u3001\u7b2c4\u5dfb\u3001100-112\u30da\u30fc\u30b8 A.Pe\u0142czy\u0144ski\uff1a \u3044\u304f\u3064\u304b\u306e\u30d0\u30ca\u30c3\u30cf\u306e\u90e8\u5c4b\u306e\u666e\u904d\u6027\u306b\u3064\u3044\u3066 \uff08\u30ed\u30b7\u30a2\u8a9e\uff09\u3001Vestnik Leningrad\u3002\u5927\u5b66\u3002 ser\u3002\u30de\u30c3\u30c8\u3002\u3042\u3042\u3002 astr\u3002 13\uff081962\uff09\u300122\u301c29\u30da\u30fc\u30b8\uff08 \u30c9\u30a4\u30c4\u8a9e\u7ffb\u8a33 ; PDF; 761 kb\uff09 P. wojtaszczyk\uff1a \u30a2\u30ca\u30ea\u30b9\u30c8\u306e\u305f\u3081\u306e\u30d0\u30ca\u30c3\u30cf\u30b9\u30da\u30fc\u30b9 \u3001Advanced Mathematics 25\uff081991\uff09\u306e\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u7814\u7a76 \u30c6\u30ea\u30fcJ.\u30e2\u30ea\u30bd\u30f3\uff1a \u6a5f\u80fd\u5206\u6790\u3001\u30d0\u30ca\u30c3\u30cf\u7a7a\u9593\u7406\u8ad6\u306e\u7d39\u4ecb \u3001Wildy-Publisher\uff082001\uff09ISBN 0471372145       (adsbygoogle = window.adsbygoogle || 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