| Title:
|
Absolute continuity with respect to a subset of an interval (English) |
| Author:
|
Loukotová, Lucie |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
327-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
absolute continuity |
| Keyword:
|
quasi-uniformity |
| Keyword:
|
acceptable mapping |
| MSC:
|
26A36 |
| MSC:
|
26A46 |
| idZBL:
|
Zbl 06837069 |
| idMR:
|
MR3708777 |
| DOI:
|
10.14712/1213-7243.2015.213 |
| . |
| Date available:
|
2017-11-22T09:22:07Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146908 |
| . |
| Reference:
|
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| . |
