[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2088#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2088","headline":"\u7a4d\u5206\u8a08\u7b97\u306e\u5e73\u5747\u5024-Wikipedia","name":"\u7a4d\u5206\u8a08\u7b97\u306e\u5e73\u5747\u5024-Wikipedia","description":"before-content-x4 \u7a4d\u5206\u8a08\u7b97\u306e\u5e73\u5747\u5024 \uff08\u307e\u305f Cauchyscher\u306e\u5e73\u5747 \u547c\u3070\u308c\u308b\uff09\u306f\u5206\u6790\u306e\u91cd\u8981\u306a\u6587\u3067\u3059\u3002\u5b9f\u969b\u306e\u5024\u3092\u8a08\u7b97\u305b\u305a\u306b\u7a4d\u5206\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5206\u6790\u306e\u57fa\u672c\u7684\u306a\u6587\u306e\u7c21\u5358\u306a\u8a3c\u62e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 \u5e73\u5747\u5024\u306e\u5e7e\u4f55\u5b66\u7684\u89e3\u91c8\u3078 g = \u521d\u3081 {displaystyleg = 1} after-content-x4 \u3002 Riemann\u7a4d\u5206\u306f\u3053\u3053\u3067\u8003\u616e\u3055\u308c\u307e\u3059\u3002\u58f0\u660e\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 after-content-x4 \u591a\u5206 f \uff1a [","datePublished":"2019-08-19","dateModified":"2019-08-19","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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3e\/MittelwertsatzIntegralrechnung.PNG\/200px-MittelwertsatzIntegralrechnung.PNG","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3e\/MittelwertsatzIntegralrechnung.PNG\/200px-MittelwertsatzIntegralrechnung.PNG","height":"251","width":"200"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2088","wordCount":6774,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u7a4d\u5206\u8a08\u7b97\u306e\u5e73\u5747\u5024 \uff08\u307e\u305f Cauchyscher\u306e\u5e73\u5747 \u547c\u3070\u308c\u308b\uff09\u306f\u5206\u6790\u306e\u91cd\u8981\u306a\u6587\u3067\u3059\u3002\u5b9f\u969b\u306e\u5024\u3092\u8a08\u7b97\u305b\u305a\u306b\u7a4d\u5206\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5206\u6790\u306e\u57fa\u672c\u7684\u306a\u6587\u306e\u7c21\u5358\u306a\u8a3c\u62e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002  \u5e73\u5747\u5024\u306e\u5e7e\u4f55\u5b66\u7684\u89e3\u91c8\u3078 g = \u521d\u3081 {displaystyleg = 1}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3002 Riemann\u7a4d\u5206\u306f\u3053\u3053\u3067\u8003\u616e\u3055\u308c\u307e\u3059\u3002\u58f0\u660e\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u591a\u5206 f \uff1a [ a \u3001 b ] \u2192 r {displaystyle fcolon [a\u3001b] to mathbb {r}} \u4e00\u5b9a\u306e\u95a2\u6570\u3082\u540c\u69d8\u3067\u3059 g \uff1a [ a \u3001 b ] \u2192 r {displaystyle gcolon [a\u3001b] to mathbb {r}} \u7d71\u5408\u53ef\u80fd\u3067\u3001\u3069\u3061\u3089\u304b g \u2265 0 {displaystyle ggeq 0} \u307e\u305f        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4g \u2264 0 {displaystyle gleq 0} \uff08\u3064\u307e\u308a\u3001\u6a19\u8b58\u304c\u5909\u66f4\u3055\u308c\u3066\u3044\u306a\u3044\uff09\u3002\u305d\u308c\u304b\u3089\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u2208 [ a \u3001 b ] {displaystyle xi in [a\u3001b]} \u3001 \u3068\u306a\u308b\u3053\u3068\u306b\u3088\u3063\u3066 \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = f \uff08 \u30d0\u30c4 \uff09\uff09 \u222b abg \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 {displaystyle int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09dx} = f\uff08xi\uff09int limits _ {a}^{b} {g\uff08x\uff09dx}}}} \u9069\u7528\u53ef\u80fd\u3067\u3059\u3002\u4e00\u90e8\u306e\u8457\u8005\u306f\u3001\u4e0a\u8a18\u306e\u58f0\u660e\u3092\u6b21\u306e\u3088\u3046\u306b\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 \u5ef6\u9577\u3055\u308c\u305f\u5e73\u5747 \u3068\u306e\u58f0\u660e g = \u521d\u3081 {displaystyleg = 1} \u3044\u3064 \u5e73\u5747 \u307e\u305f \u6700\u521d\u306e\u5e73\u5747 \u3002\u305f\u3081\u306b g = \u521d\u3081 {displaystyleg = 1} \u3042\u306a\u305f\u306f\u91cd\u8981\u306a\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3092\u53d6\u5f97\u3057\u307e\u3059\uff1a \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = f \uff08 \u30d0\u30c4 \uff09\uff09 \uff08 b  –  a \uff09\uff09 {displaystyle int limits _ {a}^{b} {f\uff08x\uff09dx} = f\uff08xi\uff09\uff08b-a\uff09} \u3001 \u5e7e\u4f55\u5b66\u7684\u306b\u7c21\u5358\u306b\u89e3\u91c8\u3067\u304d\u307e\u3059\u3002 a {displaystyle a} \u3068 b {displaystyle b} \u9577\u65b9\u5f62\u306e\u5185\u5bb9\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059 \u4e2d\u7a0b\u5ea6\u306e\u9ad8\u3055 \u3002 \u591a\u5206 g \uff08 \u30d0\u30c4 \uff09\uff09 \u2265 0 {displaystyle g\uff08x\uff09geq 0} \u9593\u9694\u3067 [ a \u3001 b ] {displaystyle [a\u3001b]} \u3002\u4ed6\u306e\u30b1\u30fc\u30b9\u306f\u3001\u79fb\u884c\u306b\u3088\u3063\u3066\u5b9f\u884c\u3067\u304d\u307e\u3059  –  g {displaystyle -g} \u3053\u308c\u306b\u8d77\u56e0\u3059\u308b\u3002 \u5b89\u5b9a\u6027\u306e\u305f\u3081 f {displaystyle f} \u306e [ a \u3001 b ] {displaystyle [a\u3001b]} \u6700\u5c0f\u304a\u3088\u3073\u6700\u5c0f\u5024\u304b\u3089\u306e\u6587\u306e\u5f8c k {displaystyle k} \u305d\u3057\u3066\u6700\u5927 k {displaystyle k} \u3067\u3002\u3068 k \u2264 f \uff08 \u30d0\u30c4 \uff09\uff09 \u2264 k {displaystyle kleq f\uff08x\uff09leq k} \u3068 g \uff08 \u30d0\u30c4 \uff09\uff09 \u2265 0 {displaystyle g\uff08x\uff09geq 0} \u306f k g \uff08 \u30d0\u30c4 \uff09\uff09 \u2264 f \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 \u2264 k g \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle kg\uff08x\uff09leq f\uff08x\uff09g\uff08x\uff09leq kg\uff08x\uff09} ; Riemann\u7a4d\u5206\u306e\u5358\u8abf\u3055\u3068\u76f4\u7dda\u6027\u306b\u3088\u308a\u3001\u3055\u3089\u306b k \u222b abg \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2264 \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2264 k \u222b abg \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 {displaystyle kint limits _ {a}^{b} {g\uff08x\uff09\u3001{rm {d}} x} int rmits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09\u3001{rm {d}} x} leq kint limits _ {x} {b} {x } x}} \u3002 \u3068 \u79c1 \uff1a= \u222b a b g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 {displaystyle i\uff1a= int limits _ {a}^{b} {g\uff08x\uff09\u3001{rm {d}} x}} \u9069\u7528\u3055\u308c\u307e\u3059 k \u79c1 \u2264 \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2264 k \u79c1 {displaystyle kileq int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09\u3001{rm {d}} x} leq ki}  \uff08\u521d\u3081\uff09 \u3002 \u3053\u308c\u3067\u3001\u6b21\u306e\u30b1\u30fc\u30b9\u3092\u533a\u5225\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u79cbi\uff1a \u79c1 \u2260 0 {displaystyle ineq 0} \u3002 – \u305d\u306e\u5f8c\u3001\u30af\u30ec\u30fc\u30e0\u306b\u306f\u540c\u7b49\u306e\u5f62\u5f0f\u304c\u3042\u308a\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 = 1Ide \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 {displaystyle f\uff08xi\uff09= {frac {1} {i}} cdot int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09\u3001{rm {d}}}}}} ; \u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u53f3\u5074\u306f\u6570\u5b57\u3067\u3042\u308a\u3001\u305d\u308c\u306f f {displaystyle f} \u306e\u305f\u3081\u306b \u30d0\u30c4 \u2208 [ a \u3001 b ] {displaystyle xi in [a\u3001b]} \u3053\u306e\u6570\u5024\u306f\u5024\u3068\u3057\u3066\u60f3\u5b9a\u3055\u308c\u307e\u3059 \uff082\uff09 \u3002 \u306a\u305c\u306a\u3089 g \uff08 \u30d0\u30c4 \uff09\uff09 \u2265 0 {displaystyle g\uff08x\uff09geq 0} \u306f 0″>\u3001\u304a\u3088\u3073\uff081\uff09\u5206\u5272\u5f8c \u79c1 {displaystyle i} \u5f62\u72b6 k \u2264 1Ide \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2264 k {displaystyle kleq {frac {1} {i}} cdot int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09\u3001{rm {d}} x} leq k} ; \u3053\u308c\u304b\u3089\uff082\uff09\u306f\u3001\u5b9a\u6570\u95a2\u6570\u306e\u4e2d\u9593\u5024\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 e\u3002 d\u3002 \u79cbII\uff1a \u79c1 = 0 {displaystyle i = 0} \u3002 – \u6b21\u306b\uff081\uff09\u306b\u5f93\u3063\u3066\u304f\u3060\u3055\u3044\uff1a \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 = 0 {displaystyle int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09\u3001{rm {d}} x} = 0} \u3001 \u305d\u3057\u3066\u3001\u4e3b\u5f35\u306f\u5f97\u3089\u308c\u307e\u3059 \u6bce\u65e5  \u30d0\u30c4 \u2208 [ a \u3001 b ] {displaystyle xi in [a\u3001b]} \u6709\u52b9\u306a\u30d5\u30a9\u30fc\u30e0 f \uff08 \u30d0\u30c4 \uff09\uff09 de 0 = 0 {displaystyle f\uff08xi\uff09cdot 0 = 0} \u3001q\u3002 e\u3002 d\u3002 \u305d\u306e\u6761\u4ef6 g \u2265 0 {displaystyle ggeq 0} \u307e\u305f  –  g \u2265 0 {displaystyle -ggeq 0} \u9069\u7528\u3055\u308c\u307e\u3059\u3002\u5b9f\u969b\u3001\u95a2\u6570\u306e\u5e73\u5747\u5024\u304c\u9069\u7528\u3055\u308c\u307e\u3059 g {displaystyle g} \u6b21\u306e\u4f8b\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u4e00\u822c\u7684\u306b\u3053\u306e\u6761\u4ef6\u304c\u3042\u308a\u307e\u305b\u3093\uff1a [ a \u3001 b ] = [  –  \u521d\u3081 \u3001 \u521d\u3081 ] {displaystyle [a\u3001b] = [-1,1]} \u3068 f \uff08 \u30d0\u30c4 \uff09\uff09 = g \uff08 \u30d0\u30c4 \uff09\uff09 = \u30d0\u30c4 {displaystyle f\uff08x\uff09= g\uff08x\uff09= x} \u306f \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 de g \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = 23{displaystyle int limits _ {a}^{b} f\uff08x\uff09cdot g\uff08x\uff09mathrm {d} x = {tfrac {2} {3}}}}} \u3001 \u3057\u304b\u3057 f \uff08 \u30d0\u30c4 \uff09\uff09 de \u222b abg \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = 0 {displaystyle f\uff08xi\uff09cdot int limits _ {a}^{b} g\uff08x\uff09mathrm {d} x = 0} \u3059\u3079\u3066\u306e\u305f\u3081\u306b \u30d0\u30c4 \u2208 [ a \u3001 b ] {displaystyle xi in [a\u3001b]} \u3002 \u306a\u308c f \u3001 g \uff1a [ a \u3001 b ] \u2192 r {displaystyle F\u3001gcolon [a\u3001b] to mathbb {r}} \u6a5f\u80fd\u3001 f {displaystyle f} \u30e2\u30ce\u30c8\u30f3\u3068 g {displaystyle g} \u5b89\u5b9a\u3002\u305d\u308c\u304b\u3089\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u2208 [ a \u3001 b ] {displaystyle xi in [a\u3001b]} \u3001 \u3068\u306a\u308b\u3053\u3068\u306b\u3088\u3063\u3066 \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 g \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = f \uff08 a \uff09\uff09 \u222b a\u03beg \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 + f \uff08 b \uff09\uff09 \u222b \u03bebg \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 {displaystyle int limits _ {a}^{b} {f\uff08x\uff09g\uff08x\uff09dx} = f\uff08a\uff09int limits _ {a}^{xi} {g\uff08x\uff09dx}+f\uff08b\uff09int limits _ {xi}^{b} {g\uff08x\uff09dx}} \u3002 \u305d\u306e\u5834\u5408\u306f f {displaystyle f} \u5e38\u306b\u5dee\u5225\u5316\u3059\u308b\u3053\u3068\u3055\u3048\u3067\u304d\u307e\u3059 \u30d0\u30c4 \u2208 \uff08 a \u3001 b \uff09\uff09 {displaystyle xi in\uff08a\u3001b\uff09} \u9078\u3076\u3002\u8a3c\u62e0\u306b\u306f\u3001\u90e8\u5206\u7684\u306a\u7d71\u5408\u3001\u5206\u6790\u306e\u57fa\u672c\u7684\u306a\u30bb\u30c3\u30c8\u3001\u4e0a\u8a18\u306e\u6587\u304c\u5fc5\u8981\u3067\u3059\u3002 \u30aa\u30c3\u30c8\u30fc\u30d5\u30a9\u30fc\u30b9\u30bf\u30fc\uff1a \u5206\u67901.\u5909\u6570\u306e\u5fae\u5206\u304a\u3088\u3073\u7a4d\u5206\u8a08\u7b97\u3002 \u7b2c7\u7248\u3002 Vieweg\u3001Braunschweig 2004\u3001ISBN 3-528-67224-2\u3002 Harro Heuser\uff1a \u5206\u6790\u306e\u6559\u79d1\u66f8 \u3002\u30d1\u30fc\u30c8\u7b2c18\u7248\u3002 B. G. Teubner\u3001Stuttgart 1990\u3001ISBN 3-519-12231-6\u3002      (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\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2088#breadcrumbitem","name":"\u7a4d\u5206\u8a08\u7b97\u306e\u5e73\u5747\u5024-Wikipedia"}}]}]