Geodesic
Absolute continuity with respect to a subset of an interval
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 327-346.

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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.
DOI : 10.14712/1213-7243.2015.213
Classification : 26A36, 26A46
Keywords: absolute continuity; quasi-uniformity; acceptable mapping 
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Loukotová, Lucie. Absolute continuity with respect to a subset of an interval. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 327-346. doi : 10.14712/1213-7243.2015.213. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.213/

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