| Title:
|
On the structure of universal differentiability sets (English) |
| Author:
|
Dymond, Michael |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
315-326 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset of $\mathbb R^{d}$ is called a universal differentiability set if it contains a point of differentiability of every Lipschitz function $f\colon\mathbb R^{d}\to \mathbb R$. We show that any universal differentiability set contains a `kernel' in which the points of differentiability of each Lipschitz function are dense. We further prove that no universal differentiability set may be decomposed as a countable union of relatively closed, non-universal differentiability sets. (English) |
| Keyword:
|
differentiability |
| Keyword:
|
Lipschitz functions |
| Keyword:
|
universal differentiability set |
| Keyword:
|
$\sigma$-porous set |
| MSC:
|
46G05 |
| MSC:
|
46T20 |
| idZBL:
|
Zbl 06837068 |
| idMR:
|
MR3708776 |
| DOI:
|
10.14712/1213-7243.2015.218 |
| . |
| Date available:
|
2017-11-01T16:51:21Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146910 |
| . |
| Reference:
|
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| . |
