叶果洛夫定理的一个新证明

A New Proof of Egoroff Theorem

介绍了叶果洛夫定理的一个新证明 ,所得的主要结果是 :刻划几乎处处收敛的可测函数列的引理1,刻划几乎一致收敛的可测函数列的引理 2 ,定理 1(叶果洛夫定理 )和定理 2 (叶果洛夫定理之逆 ) .

In this paper, a new proof of E goroff theorem is given. The main results are as follows: Lemma 1 characterizes series of measurable functions which are convergent almo st everywhere, Lemma 2 characterizes series of measurable functions which are convergent almost uniformly, theorem 1 and its inverse, theorem 2 give a new pro of of well-known Egoroff theorem.