| Title:
|
Sets of extended uniqueness and $\sigma$-porosity (English) |
| Author:
|
Zelený, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
337-341 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that there exists a closed non-$\sigma$-porous set of extended uniqueness. We also give a new proof of Lyons' theorem, which shows that the class of $H^{(n)}$-sets is not large in $U_0$. (English) |
| Keyword:
|
$\sigma $-porosity |
| Keyword:
|
sets of extended uniqueness |
| Keyword:
|
trigonometric series |
| Keyword:
|
$H^{(n)}$-sets |
| MSC:
|
28A05 |
| MSC:
|
42A63 |
| MSC:
|
43A46 |
| idZBL:
|
Zbl 0894.28001 |
| idMR:
|
MR1455500 |
| . |
| Date available:
|
2009-01-08T18:31:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118931 |
| . |
| Reference:
|
[BKR] Bukovský L., Kholshchevnikova N.N., Repický M.: Thin sets of harmonic analysis and infinite combinatorics.Real Analysis Exchange 20.2 (1994-95), 454-509. MR 1348075 |
| Reference:
|
[DSR] Debs G., Saint-Raymond J.: Ensembles boréliens d'unicité et d'unicité au sens large.Ann. Inst. Fourier (Grenoble) 37 (1987), 217-239. MR 0916281 |
| Reference:
|
[D] Dolzhenko E.P.: Boundary properties of arbitrary functions (in Russian).Izv. Akad. Nauk. SSSR Ser. Mat. 31 (1967), 3-14. MR 0217297 |
| Reference:
|
[KL] Kechris A., Louveau A.: Descriptive Set Theory and the Structure of Sets of Uniqueness.Cambridge U. Press, Cambridge (1987). Zbl 0642.42014, MR 0953784 |
| Reference:
|
[L] Lyons R.: The size of some classes of thin sets.Studia Math. 86.1 (1987), 59-78. Zbl 0628.43006, MR 0887312 |
| Reference:
|
[T] Tkadlec J.: Construction of a finite Borel measure with $\sigma$-porous sets as null sets.Real Analysis Exchange 12 (1986-87), 349-353. Zbl 0649.28005, MR 0873903 |
| Reference:
|
[Š] Šleich P.: Sets of type $H^{(s)}$ are $\sigma$-bilaterally porous.unpublished. |
| Reference:
|
[Z$_1$] Zajíček L.: Sets of $\sigma$-porosity and sets of $\sigma$-porosity(q).Časopis Pěst. Mat. 101 (1976), 350-359. Zbl 0341.30026, MR 0457731 |
| Reference:
|
[Z$_2$] Zajíček L.: Porosity and $\sigma$-porosity.Real Analysis Exchange 13 (1987-88), 314-350. MR 0943561 |
| Reference:
|
[Z$_3$] Zajíček L.: A note on $\sigma$-porous sets.Real Analysis Exchange 17.1 (1991-92), 18. |
| . |
