A criterion for absolute continuity

被引：0
|
作者：
Kowalczyk, Stanislaw [1 ]
Ponomarev, Stanislav [1 ]
机构：
[1] Pomeranian Acad Slupsk, Inst Math, PL-76200 Slupsk, Poland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 90卷
关键词：
Absolute continuity; Lebesgue point; Riesz representation theorem; Hahn-Banach theorem; Du Bois-Reymond theorem; Fubini's theorem;
D O I：
10.1016/j.na.2013.05.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A necessary and sufficient condition for a summable function f is an element of L([a, b]) to be equivalent to an absolutely continuous (AC) function is given. Our method is based uniquely on evaluation of integrals and not on classical "epsilon-delta" definitions. A condition for the existence of an AC function is discussed. Also the case of functions of many variables is studied. (C) 2013 Elsevier Ltd. All rights reserved.
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页码：113 / 120
页数：8
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