[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/5022#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/5022","headline":"\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406 – Wikipedia","name":"\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406 – Wikipedia","description":"\u6570\u5b66\u306b\u304a\u3051\u308b\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\uff08\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u3066\u3044\u308a\u3001\u82f1: Radon\u2013Nikod\u00fdm theorem\uff09\u306f\u3001\u6e2c\u5ea6\u8ad6\u306e\u5206\u91ce\u306b\u304a\u3051\u308b\u4e00\u7d50\u679c\u3067\u3001\u3042\u308b\u53ef\u6e2c\u7a7a\u9593 (X, \u03a3) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001(X, \u03a3) \u4e0a\u306e\u3042\u308b \u03c3-\u6709\u9650\u6e2c\u5ea6\uff08\u82f1\u8a9e\u7248\uff09 \u03bd \u304c\u5225\u306e (X, \u03a3) \u4e0a\u306e \u03c3-\u6709\u9650\u6e2c\u5ea6 \u03bc \u306b\u95a2\u3057\u3066\u7d76\u5bfe\u9023\u7d9a\u3067\u3042\u308b\u306a\u3089\u3001\u4efb\u610f\u306e\u53ef\u6e2c\u90e8\u5206\u96c6\u5408 A \u2282 X","datePublished":"2019-02-26","dateModified":"2019-02-26","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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\/d89508d4f8368d8d47ef131f6790a58cc9cc027d","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d89508d4f8368d8d47ef131f6790a58cc9cc027d","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/5022","about":["Wiki"],"wordCount":8819,"articleBody":"\u6570\u5b66\u306b\u304a\u3051\u308b\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\uff08\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u3066\u3044\u308a\u3001\u82f1: Radon\u2013Nikod\u00fdm theorem\uff09\u306f\u3001\u6e2c\u5ea6\u8ad6\u306e\u5206\u91ce\u306b\u304a\u3051\u308b\u4e00\u7d50\u679c\u3067\u3001\u3042\u308b\u53ef\u6e2c\u7a7a\u9593 (X, \u03a3) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001(X, \u03a3) \u4e0a\u306e\u3042\u308b \u03c3-\u6709\u9650\u6e2c\u5ea6\uff08\u82f1\u8a9e\u7248\uff09 \u03bd \u304c\u5225\u306e (X, \u03a3) \u4e0a\u306e \u03c3-\u6709\u9650\u6e2c\u5ea6 \u03bc \u306b\u95a2\u3057\u3066\u7d76\u5bfe\u9023\u7d9a\u3067\u3042\u308b\u306a\u3089\u3001\u4efb\u610f\u306e\u53ef\u6e2c\u90e8\u5206\u96c6\u5408 A \u2282 X \u306b\u5bfe\u3057\u3066\u6b21\u3092\u6e80\u305f\u3059\u53ef\u6e2c\u51fd\u6570 \u2009f\u2009\u00a0: X \u2192 [0, \u221e) \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u8ff0\u3079\u305f\u5b9a\u7406\u3067\u3042\u308b\uff1a\u03bd(A)=\u222bAfd\u03bc{displaystyle nu (A)=int _{A}f,dmu }  \u3053\u306e\u51fd\u6570 \u2009f\u2009 \u306f\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206\u3068\u547c\u3070\u308c\u3001d\u03bd\/d\u03bc \u3068\u8868\u8a18\u3055\u308c\u308b\u3002\u3053\u306e\u5b9a\u7406\u306e\u540d\u306f\u30011913\u5e74\u306b\u7a7a\u9593 RN \u3067\u306e\u7279\u5225\u306a\u5834\u5408\u306b\u3064\u3044\u3066\u8a3c\u660e\u3092\u4e0e\u3048\u305f\u30e8\u30cf\u30f3\u30fb\u30e9\u30c9\u30f3\uff08\u82f1\u8a9e\u7248\uff09\u3068\u30011930\u5e74\u306b\u4e00\u822c\u306e\u5834\u5408\u306e\u8a3c\u660e\u3092\u4e0e\u3048\u305f\u30aa\u30c3\u30c8\u30fc\u30fb\u30cb\u30b3\u30c7\u30a3\u30e0\uff08\u82f1\u8a9e\u7248\uff09\u306b\u7531\u6765\u3059\u308b[1]\u30021936\u5e74\u306b\u30cf\u30f3\u30b9\u30fb\u30d5\u30ed\u30a4\u30c7\u30f3\u30bf\u30fc\u30eb\u306f\u3001\u3053\u306e\u5b9a\u7406\u3092\u7279\u5225\u306a\u5834\u5408\u3068\u3057\u3066\u542b\u3080\u3001\u30ea\u30fc\u30b9\u7a7a\u9593\u3067\u306e\u4e00\u7d50\u679c\u3067\u3042\u308b\u30d5\u30ed\u30a4\u30c7\u30f3\u30bf\u30fc\u30eb\u306e\u30b9\u30da\u30af\u30c8\u30eb\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u305d\u306e\u7d50\u679c\u306e\u66f4\u306a\u308b\u4e00\u822c\u5316\u306b\u6210\u529f\u3057\u305f[2]\u3002  Y \u304c\u30d0\u30ca\u30c3\u30cf\u7a7a\u9593\u3067\u3042\u308a\u3001\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\u304c Y \u306b\u5024\u3092\u53d6\u308b\u51fd\u6570\u306b\u5bfe\u3057\u3066\u540c\u69d8\u306b\u6210\u308a\u7acb\u3064\u306a\u3089\u3001Y \u306f\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u6027\u3092\u5099\u3048\u308b\u3068\u8a00\u308f\u308c\u308b\u3002\u5168\u3066\u306e\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u306f\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u6027\u3092\u5099\u3048\u3066\u3044\u308b\u3002Table of Contents\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206[\u7de8\u96c6]\u3055\u3089\u306a\u308b\u5fdc\u7528[\u7de8\u96c6]\u60c5\u5831\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9[\u7de8\u96c6]\u03c3-\u6709\u9650\u6027\u306e\u4eee\u5b9a[\u7de8\u96c6]\u6709\u9650\u6e2c\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]\u03c3-\u6709\u9650\u6b63\u6e2c\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]\u7b26\u53f7\u4ed8\u6e2c\u5ea6\u304a\u3088\u3073\u8907\u7d20\u6e2c\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206[\u7de8\u96c6]\u4e0a\u8ff0\u306e\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u51fd\u6570 \u2009f\u2009 \u306f\u3001 \u03bc-\u96f6\u96c6\u5408\u306e\u9055\u3044\u3092\u9664\u3044\u3066\u4e00\u610f\u3067\u3042\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u540c\u3058\u6027\u8cea\u3092\u6e80\u305f\u3059\u5225\u306e\u51fd\u6570 g \u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3001\u03bc \u306b\u95a2\u3057\u3066\u307b\u3068\u3093\u3069\u81f3\u308b\u3068\u3053\u308d\u3067 \u2009f\u2009 = g \u304c\u6210\u308a\u7acb\u3064\u3002\u2009f\u2009 \u306f\u901a\u5e38 d\u03bd\/d\u03bc \u3068\u8868\u8a18\u3055\u308c\u3001\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u306e\u8868\u8a18\u3068\u547c\u79f0\u306f\u3001\u3053\u306e\u51fd\u6570\u304c\u3042\u308b\u6e2c\u5ea6\u306e\u5225\u306e\u6e2c\u5ea6\u306b\u95a2\u3059\u308b\u5bc6\u5ea6\u306e\u5909\u5316\u7387\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u5fae\u5206\u7a4d\u5206\u5b66\u306b\u304a\u3051\u308b\u5fae\u5206\u306e\u985e\u4f3c\u7269\u3068\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u306b\u7531\u6765\u3059\u308b\u3002\u540c\u69d8\u306e\u5b9a\u7406\u306f\u3001\u7b26\u53f7\u4ed8\u8907\u7d20\u6e2c\u5ea6\u306b\u5bfe\u3057\u3066\u3082\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u03bc \u304c\u975e\u8ca0\u306e \u03c3-\u6709\u9650\u6e2c\u5ea6\u3067\u3001\u03bd \u304c\u6709\u9650\u5024\u306e\u7b26\u53f7\u4ed8\u3042\u308b\u3044\u306f\u8907\u7d20\u6e2c\u5ea6\u3067 |\u03bd| \u226a \u03bc \u3092\u6e80\u305f\u3059\uff08\u03bd \u304c \u03bc \u306b\u95a2\u3057\u3066\u7d76\u5bfe\u9023\u7d9a\u3067\u3042\u308b\uff09\u306a\u3089\u3001X \u4e0a\u306e \u03bc-\u53ef\u7a4d\u5206\u306a\u5b9f\u3042\u308b\u3044\u306f\u8907\u7d20\u6570\u5024\u51fd\u6570 g \u304c\u5b58\u5728\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u53ef\u6e2c\u96c6\u5408 A \u306b\u5bfe\u3057\u3066\u6b21\u3092\u6e80\u305f\u3059\u3002  \u03bd(A)=\u222bAgd\u03bc.{displaystyle nu (A)=int _{A}g,dmu .}\u3053\u306e\u5b9a\u7406\u306f\u78ba\u7387\u8ad6\u306b\u304a\u3051\u308b\u30a2\u30a4\u30c7\u30a2\u3092\u3001\u5b9f\u6570\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u78ba\u7387\u8cea\u91cf\u304a\u3088\u3073\u78ba\u7387\u5bc6\u5ea6\u304b\u3089\u3001\u4efb\u610f\u306e\u96c6\u5408\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u78ba\u7387\u6e2c\u5ea6\u3078\u3068\u62e1\u5f35\u3059\u308b\u4e0a\u3067\u975e\u5e38\u306b\u91cd\u8981\u3068\u306a\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u3001\u3042\u308b\u78ba\u7387\u6e2c\u5ea6\u3092\u5225\u306e\u3082\u306e\u3078\u5909\u5316\u3055\u305b\u308b\u3053\u3068\u304c\u53ef\u80fd\u304b\u3001\u307e\u305f\u53ef\u80fd\u3067\u3042\u308c\u3070\u3069\u306e\u3088\u3046\u306b\u3067\u304d\u308b\u304b\u3001\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002\u7279\u306b\u3001\u3042\u308b\u78ba\u7387\u5909\u6570\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u3001\u3042\u308b\u57fa\u5e95\u6e2c\u5ea6\uff08\u901a\u5e38\u306f\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u306b\u5bfe\u3059\u308b\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6\uff09\u306b\u95a2\u3059\u308b\u8a98\u5c0e\u6e2c\u5ea6 (induced measure) \u306e\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206\u3068\u306a\u308b\u3002\u305d\u308c\u306f\u4f8b\u3048\u3070\u3001\u78ba\u7387\u6e2c\u5ea6\u306e\u6761\u4ef6\u4ed8\u671f\u5f85\u5024\u306e\u5b58\u5728\u3092\u793a\u3059\u969b\u306b\u5229\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304c\u3001\u3053\u308c\u81ea\u4f53\u304c\u78ba\u7387\u8ad6\u306b\u304a\u3051\u308b\u91cd\u8981\u6982\u5ff5\u3067\u3042\u308a\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u305d\u306e\u7279\u6b8a\u4f8b\u306b\u904e\u304e\u306a\u3044\u3002\u305d\u306e\u4ed6\u306e\u5206\u91ce\u3067\u306f\u3001\u6570\u7406\u30d5\u30a1\u30a4\u30ca\u30f3\u30b9\u306b\u304a\u3044\u3066\u3053\u306e\u5b9a\u7406\u306f\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u3002\u78ba\u7387\u6e2c\u5ea6\u306e\u5909\u5316\u306f\u30c7\u30ea\u30d0\u30c6\u30a3\u30d6\u306e\u5408\u7406\u4fa1\u683c\u8a2d\u5b9a (rational pricing) \u3092\u884c\u3046\u4e0a\u3067\u306e\u57fa\u672c\u3067\u3042\u308a\u3001\u5b9f\u969b\u306e\u78ba\u7387\u3092\u30ea\u30b9\u30af\u4e2d\u7acb\u78ba\u7387\u306b\u8ee2\u63db\u3059\u308b\u4e0a\u3067\u7528\u3044\u3089\u308c\u308b\u3002\u03bd, \u03bc \u304a\u3088\u3073 \u03bb \u3092\u540c\u4e00\u306e\u6e2c\u5ea6\u7a7a\u9593\u4e0a\u306e \u03c3-\u6709\u9650\u6e2c\u5ea6\u3068\u3059\u308b\u3002\u03bd \u226a \u03bb \u304a\u3088\u3073 \u03bc \u226a \u03bb\uff08\u03bd \u3068 \u03bc \u306f \u03bb \u306b\u95a2\u3057\u3066\u7d76\u5bfe\u9023\u7d9a\uff09\u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002d(\u03bd+\u03bc)d\u03bb=d\u03bdd\u03bb+d\u03bcd\u03bb\u03bb-almost everywhere.{displaystyle {frac {d(nu +mu )}{dlambda }}={frac {dnu }{dlambda }}+{frac {dmu }{dlambda }}quad lambda {text{-almost everywhere}}.}\u03bd \u226a \u03bc \u226a \u03bb \u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002d\u03bdd\u03bb=d\u03bdd\u03bcd\u03bcd\u03bb\u03bb-almost everywhere.{displaystyle {frac {dnu }{dlambda }}={frac {dnu }{dmu }}{frac {dmu }{dlambda }}quad lambda {text{-almost everywhere}}.}\u7279\u306b\u3001\u03bc \u226a \u03bd \u304b\u3064 \u03bd \u226a \u03bc \u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002d\u03bcd\u03bd=(d\u03bdd\u03bc)\u22121\u03bd-almost everywhere.{displaystyle {frac {dmu }{dnu }}=left({frac {dnu }{dmu }}right)^{-1}quad nu {text{-almost everywhere}}.}\u03bc \u226a \u03bb \u3067\u3042\u308a\u3001g \u304c \u03bc-\u53ef\u7a4d\u5206\u51fd\u6570\u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002\u222bXgd\u03bc=\u222bXgd\u03bcd\u03bbd\u03bb.{displaystyle int _{X}g,dmu =int _{X}g{frac {dmu }{dlambda }},dlambda .}\u03bd \u304c\u6709\u9650\u306e\u7b26\u53f7\u4ed8\u6e2c\u5ea6\u3042\u308b\u3044\u306f\u8907\u7d20\u6e2c\u5ea6\u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002d|\u03bd|d\u03bc=|d\u03bdd\u03bc|.{displaystyle {d|nu | over dmu }=left|{dnu  over dmu }right|.}\u3055\u3089\u306a\u308b\u5fdc\u7528[\u7de8\u96c6]\u60c5\u5831\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9[\u7de8\u96c6]\u03bc \u304a\u3088\u3073 \u03bd \u306f X \u4e0a\u306e\u6e2c\u5ea6\u3067\u3001\u03bc \u226a \u03bd \u304c\u6210\u308a\u7acb\u3064\u3082\u306e\u3068\u3059\u308b\u3002DKL(\u03bc\u2016\u03bd)=\u222bXlog\u2061(d\u03bcd\u03bd)d\u03bc.{displaystyle D_{mathrm {KL} }(mu |nu )=int _{X}log left({frac {dmu }{dnu }}right);dmu .}D\u03b1(\u03bc\u2016\u03bd)=1\u03b1\u22121log\u2061(\u222bX(d\u03bcd\u03bd)\u03b1\u22121d\u03bc).{displaystyle D_{alpha }(mu |nu )={frac {1}{alpha -1}}log left(int _{X}left({frac {dmu }{dnu }}right)^{alpha -1};dmu right).}\u03c3-\u6709\u9650\u6027\u306e\u4eee\u5b9a[\u7de8\u96c6]\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\u3067\u306f\u3001\u03bd \u306e\u5909\u5316\u306e\u5272\u5408\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u6e2c\u5ea6 \u03bc \u306f \u03c3-\u6709\u9650\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3055\u308c\u3066\u3044\u305f\u3002\u3053\u3053\u3067\u306f\u3001\u305d\u306e \u03bc \u304c \u03c3-\u6709\u9650\u3067\u306a\u3044\u3068\u304d\u306b\u306f\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\u304c\u6210\u7acb\u3057\u306a\u3044\u3053\u3068\u3092\u793a\u3059\u3002\u5b9f\u6570\u76f4\u7dda\u4e0a\u306e\u30dc\u30ec\u30eb\u5b8c\u5168\u52a0\u6cd5\u65cf\u3092\u8003\u3048\u308b\u3002\u3042\u308b\u30dc\u30ec\u30eb\u96c6\u5408 A \u306e\u6570\u3048\u4e0a\u3052\u6e2c\u5ea6 \u03bc \u3092\u3001A \u304c\u6709\u9650\u3067\u3042\u308b\u5834\u5408\u306f\u305d\u306e\u5143\u306e\u6570\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f \u221e \u3067\u5b9a\u7fa9\u3059\u308b\u3002\u5b9f\u969b\u306b \u03bc \u304c\u6e2c\u5ea6\u3067\u3042\u308b\u3053\u3068\u306f\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u3002\u3057\u304b\u3057\u3001\u3059\u3079\u3066\u306e\u30dc\u30ec\u30eb\u96c6\u5408\u304c\u6709\u9650\u96c6\u5408\u306e\u53ef\u7b97\u500b\u306e\u5408\u4f75\u3067\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u306e\u3067\u3001\u305d\u308c\u306f \u03c3-\u6709\u9650\u3067\u306f\u306a\u3044\u3002\u03bd \u3092\u3053\u306e\u30dc\u30ec\u30eb\u52a0\u6cd5\u65cf\u4e0a\u306e\u901a\u5e38\u306e\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u03bd \u306f \u03bc \u306b\u95a2\u3057\u3066\u7d76\u5bfe\u9023\u7d9a\u3067\u3042\u308b\u3002\u306a\u305c\u306a\u3089\u3001\u3042\u308b\u96c6\u5408 A \u306b\u5bfe\u3057\u3066 \u03bc(A) = 0 \u3068\u306a\u308b\u306e\u306f A \u304c\u7a7a\u96c6\u5408\u3067\u3042\u308b\u3068\u304d\u306e\u307f\u3067\u3042\u308a\u3001\u305d\u306e\u3068\u304d\u306f \u03bd(A) \u3082\u30bc\u30ed\u3068\u306a\u308b\u304b\u3089\u3067\u3042\u308b\u3002\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\u304c\u6210\u7acb\u3059\u308b\u3082\u306e\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u3042\u308b\u53ef\u6e2c\u51fd\u6570 \u2009f\u2009 \u306b\u5bfe\u3057\u3066\u03bd(A)=\u222bAfd\u03bc{displaystyle nu (A)=int _{A}f,dmu }\u304c\u3059\u3079\u3066\u306e\u30dc\u30ec\u30eb\u96c6\u5408\u306b\u3064\u3044\u3066\u6210\u7acb\u3059\u308b\u3082\u306e\u3068\u3059\u308b\u3002A \u3092\u5358\u96c6\u5408 A = {a} \u3068\u3057\u3001\u4e0a\u8ff0\u306e\u7b49\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u30670=f(a){displaystyle 0=f(a)}\u304c\u3059\u3079\u3066\u306e\u5b9f\u6570 a \u306b\u5bfe\u3057\u3066\u6210\u308a\u7acb\u3064\u3002\u3053\u306e\u3053\u3068\u306f\u51fd\u6570 \u2009f\u2009 \u304a\u3088\u3073\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6 \u03bd \u304c\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u77db\u76fe\u3067\u3042\u308b\u3002\u3053\u306e\u7bc0\u3067\u306f\u3001\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406\u306e\u6e2c\u5ea6\u8ad6\u7684\u306a\u8a3c\u660e\u3092\u7d39\u4ecb\u3059\u308b\u3002\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u306e\u624b\u6cd5\u3092\u4f7f\u3063\u305f\u51fd\u6570\u89e3\u6790\u7684\u306a\u8a3c\u660e\u3082\u3001\u30b8\u30e7\u30f3\u30fb\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3002\u8a3c\u660e\u306e\u30a2\u30a4\u30c7\u30a2\u306f\u3001\u6709\u9650\u6e2c\u5ea6 \u03bc \u304a\u3088\u3073 \u03bd \u306b\u5bfe\u3057\u3066 \u2009f\u2009d\u03bc \u2264 d\u03bd \u3092\u6e80\u305f\u3059\u51fd\u6570 \u2009f\u2009 \u3092\u8003\u3048\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u5358\u8abf\u53ce\u675f\u5b9a\u7406\u306e\u4e0b\u3067\u3001\u305d\u306e\u3088\u3046\u306a\u3059\u3079\u3066\u306e\u51fd\u6570\u306e\u4e0a\u9650\u306f\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u5fae\u5206\u3092\u4e0e\u3048\u308b\u3002\u6709\u9650\u6e2c\u5ea6\u306b\u95a2\u3059\u308b\u6280\u8853\u7684\u306a\u4e8b\u5b9f\u3088\u308a\u3001\u03bc \u306e\u6b8b\u308a\u306e\u90e8\u5206\u306f \u03bd \u306b\u95a2\u3057\u3066\u7279\u7570\u7684\u3067\u3042\u308b\u3053\u3068\u304c\u5f93\u3046\u3002\u305d\u306e\u3088\u3046\u306a\u7d50\u679c\u304c\u6709\u9650\u6e2c\u5ea6\u306b\u5bfe\u3057\u3066\u5f97\u3089\u308c\u308c\u3070\u3001\u03c3-\u6709\u9650\u6e2c\u5ea6\u3084\u7b26\u53f7\u4ed8\u6e2c\u5ea6\u3001\u8907\u7d20\u6e2c\u5ea6\u306b\u5bfe\u3057\u3066\u3082\u81ea\u7136\u306a\u5f62\u3067\u62e1\u5f35\u3055\u308c\u308b\u3002\u8a73\u7d30\u306f\u4e0b\u8a18\u306e\u901a\u308a\u3067\u3042\u308b\u3002\u6709\u9650\u6e2c\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]\u306f\u3058\u3081\u306b \u03bc \u3068 \u03bd \u306e\u3044\u305a\u308c\u3082\u6709\u9650\u5024\u306e\u975e\u8ca0\u6e2c\u5ea6\u3067\u3042\u308b\u5834\u5408\u3092\u8003\u3048\u308b\u3002F \u3092\u3001\u6b21\u306e\u95a2\u4fc2\u5f0f\u3092\u6e80\u305f\u3059\u3088\u3046\u306a\u305d\u308c\u3089\u306e\u53ef\u6e2c\u51fd\u6570 \u2009f\u2009\u00a0: X \u2192 [0, \u221e) \u306e\u96c6\u5408\u3068\u3059\u308b\uff1a\u2200A\u2208\u03a3:\u222bAfd\u03bc\u2264\u03bd(A).{displaystyle forall Ain Sigma :qquad int _{A}f,dmu leq nu (A).}\u5c11\u306a\u304f\u3068\u3082\u30bc\u30ed\u51fd\u6570\u3092\u542b\u3080\u305f\u3081 F \u2260 \u2205 \u3067\u3042\u308b\u3002\u4eca \u2009f1, \u2009f2 \u2208 F \u3068\u3057\u3001A \u3092\u4efb\u610f\u306e\u53ef\u6e2c\u96c6\u5408\u3068\u3057\u3001\u6b21\u3092\u5b9a\u7fa9\u3059\u308b\uff1a"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/5022#breadcrumbitem","name":"\u30e9\u30c9\u30f3\uff1d\u30cb\u30b3\u30c7\u30a3\u30e0\u306e\u5b9a\u7406 – Wikipedia"}}]}]