| Title:
|
Strong measure zero and meager-additive sets through the prism of fractal measures (English) |
| Author:
|
Zindulka, Ondřej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
131-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We develop a theory of sharp measure zero sets that parallels Borel's strong measure zero, and prove a theorem analogous to Galvin--Mycielski--Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of $2^{\omega}$ is meager-additive if and only if it is $\mathcal E$-additive; if $f\colon 2^{\omega}\to 2^{\omega}$ is continuous and $X$ is meager-additive, then so is $f(X)$. (English) |
| Keyword:
|
meager-additive |
| Keyword:
|
$\mathcal E$-additive |
| Keyword:
|
strong measure zero |
| Keyword:
|
sharp measure zero |
| Keyword:
|
Hausdorff dimension |
| Keyword:
|
Hausdorff measure |
| MSC:
|
03E05 |
| MSC:
|
03E20 |
| MSC:
|
28A78 |
| idZBL:
|
Zbl 07088828 |
| idMR:
|
MR3946667 |
| DOI:
|
10.14712/1213-7243.2015.277 |
| . |
| Date available:
|
2019-05-13T07:52:02Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147668 |
| . |
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