Moduli of Continuity and Absolute Continuity: Any Relation?

被引：0
|
作者：
Muratori, Matteo [1 ]
Somaglia, Jacopo [1 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
来源：
RESULTS IN MATHEMATICS | 2025年 / 80卷 / 01期
关键词：
Absolute continuity; modulus of continuity; cantor function;
D O I：
10.1007/s00025-025-02353-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function and the absolute continuity of its modulus of continuity, in contrast with a well-known property of Lipschitz functions.
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页数：9
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