Lucie Loukotov√°
Absolute continuity with respect to a subset of an interval

Comment.Math.Univ.Carolin. 58,3 (2017) 327-346.

Abstract:The aim of this paper is to introduce a generalization of the classical absolute continuity to a relative case, with respect to a subset $M$ of an interval~ $I$. This generalization is based on adding more requirements to disjoint systems $\{(a_k, b_k)\}_K$ from the classical definition of absolute continuity -- these systems should be not too far from $M$ and should be small relative to some covers of $M$. We discuss basic properties of relative absolutely continuous functions and compare this class with other classes of generalized absolutely continuous functions.

Keywords: absolute continuity; quasi-uniformity; acceptable mapping

DOI: DOI 10.14712/1213-7243.2015.213
AMS Subject Classification: 26A46 26A36