CAJ | 학술논문

　　基于叶果罗夫定理，考虑 Lebesgue 积分序列的收敛性，证明了一致绝对连续可积函数序列的处处收敛性，通过分析Sobolev空间逼近函数列的性质，发现了它的一致绝对连续性以及相应积分序列的收敛性，证明了 Sobolev 空间中的函数可以被一致绝对连续函数列逼近。因此只要函数列一致绝对连续可积，就足以保证积分序列的收敛，最后举例进行了说明。
　　기우협과라부정리，고필 Lebesgue 적분서렬적수렴성，증명료일치절대련속가적함수서렬적처처수렴성，통과분석Sobolev공간핍근함수렬적성질，발현료타적일치절대련속성이급상응적분서렬적수렴성，증명료 Sobolev 공간중적함수가이피일치절대련속함수렬핍근。인차지요함수렬일치절대련속가적，취족이보증적분서렬적수렴，최후거례진행료설명。
Based on the Eropob-theorm, the article considers sequences of Lebesgue imegrable functions, and proves that the a.e. convergence of a sequence of uniformly absolute continuously integrable functions implies the convergence of the sequence of their integration, anlysises deeply that Sobolev-space function’s characters,discovers that the uniformly absolute continuous and coresponding convergence of an integration sequence, and further proves that any function in Sobolev-space can be approximated by a sequence of uniformly absolute continuously integrable functions. The concolusion of the article is that a sequence of uniformly absolute continuously integrable functions implies the convergence of the sequence .An examples is given to illustrate their applications.