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測(cè)度

時(shí)間:2023-03-07 08:20:17 數(shù)學(xué)畢業(yè)論文 我要投稿
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關(guān)于測(cè)度

關(guān)于測(cè)度


摘要:本文主要通過說明黎曼積分的局限性,引入1種新的劃分,導(dǎo)出勒貝格測(cè)度的概念,繼而重點(diǎn)討論勒貝格測(cè)度的性質(zhì).最后總結(jié)勒貝格可測(cè)集類和介紹構(gòu)造 上勒貝格不可測(cè)集的方法,并給出了1個(gè) 上不可測(cè)集的例子.

關(guān)鍵字:黎曼積分;勒貝格測(cè)度;可測(cè)集;不可測(cè)集

About Measure


Abstract: In this paper, the limitation in the application of  the Riemann integral is pointed out, and the Lebesgue Measure is educed by introducing a new partition, and the Messurable Set and the Unmeasured Set are mainly discussed. In the end, the method to construst a Unmeasured Set in  is obtained,and a example of Unmeasured Set in   is given.
Keywords: Riemann integral; Lebesgue Measure; Messurable Set; Unmeasured Set