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數(shù)學(xué)瘋子新蟲(chóng) (初入文壇)
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[求助]
實(shí)變中的主要定理的證明思路基本就是利特伍德說(shuō)過(guò)的3個(gè)準(zhǔn)則
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實(shí)變中的主要定理的證明思路基本就是利特伍德說(shuō)過(guò)的3個(gè)準(zhǔn)則 請(qǐng)問(wèn)這三個(gè)準(zhǔn)則是什么?求解析,謝謝了 |
鐵桿木蟲(chóng) (著名寫(xiě)手)
帶你飛翔
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1)任一可測(cè)集差不多就是開(kāi)集(至多可數(shù)個(gè)開(kāi)區(qū)間的并)。 2)任一可測(cè)函數(shù)差不多就是連續(xù)函數(shù)。(Lusin定理) 3)任一pointwise收斂的可測(cè)函數(shù)列差不多就是uniform收斂的。(Egorov定理) Littlewood stated the principles in his 1944 Lectures on the Theory of Functions [1] as: There are three principles, roughly expressible in the following terms: Every (measurable) set is nearly a finite sum of intervals; every function (of class Lλ) is nearly continuous; every convergent sequence of functions is nearly uniformly convergent. The first principle is based on the fact that the inner measure and outer measure are equal for measurable sets, the second is based on Lusin's theorem, and the third is based on Egorov's theorem. |

新蟲(chóng) (初入文壇)

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