Absolute continuity with respect to a subset of an interval

Lucie Loukotová

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 3, page 327-346
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Loukotová, Lucie. "Absolute continuity with respect to a subset of an interval." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 327-346. <http://eudml.org/doc/294145>.

@article{Loukotová2017,
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 $\lbrace (a_k, b_k)\rbrace _K$ 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.},
author = {Loukotová, Lucie},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {absolute continuity; quasi-uniformity; acceptable mapping},
language = {eng},
number = {3},
pages = {327-346},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Absolute continuity with respect to a subset of an interval},
url = {http://eudml.org/doc/294145},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Loukotová, Lucie
TI - Absolute continuity with respect to a subset of an interval
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 327
EP - 346
AB - 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 $\lbrace (a_k, b_k)\rbrace _K$ 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.
LA - eng
KW - absolute continuity; quasi-uniformity; acceptable mapping
UR - http://eudml.org/doc/294145
ER -

References

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