Sets of extended uniqueness and σ -porosity

Miroslav Zelený

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 337-341
  • ISSN: 0010-2628

Abstract

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We show that there exists a closed non- σ -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 .

How to cite

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Zelený, Miroslav. "Sets of extended uniqueness and $\sigma $-porosity." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 337-341. <http://eudml.org/doc/248049>.

@article{Zelený1997,
abstract = {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 $U_0$.},
author = {Zelený, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\sigma $-porosity; sets of extended uniqueness; trigonometric series; $H^\{(n)\}$-sets; -porosity; sets of extended uniqueness},
language = {eng},
number = {2},
pages = {337-341},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sets of extended uniqueness and $\sigma $-porosity},
url = {http://eudml.org/doc/248049},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Zelený, Miroslav
TI - Sets of extended uniqueness and $\sigma $-porosity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 337
EP - 341
AB - We show that there exists a closed non-$\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 $U_0$.
LA - eng
KW - $\sigma $-porosity; sets of extended uniqueness; trigonometric series; $H^{(n)}$-sets; -porosity; sets of extended uniqueness
UR - http://eudml.org/doc/248049
ER -

References

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  2. Debs G., Saint-Raymond J., Ensembles boréliens d'unicité et d'unicité au sens large, Ann. Inst. Fourier (Grenoble) 37 (1987), 217-239. (1987) MR0916281
  3. Dolzhenko E.P., Boundary properties of arbitrary functions (in Russian), Izv. Akad. Nauk. SSSR Ser. Mat. 31 (1967), 3-14. (1967) MR0217297
  4. Kechris A., Louveau A., Descriptive Set Theory and the Structure of Sets of Uniqueness, Cambridge U. Press, Cambridge (1987). (1987) Zbl0642.42014MR0953784
  5. Lyons R., The size of some classes of thin sets, Studia Math. 86.1 (1987), 59-78. (1987) Zbl0628.43006MR0887312
  6. Tkadlec J., Construction of a finite Borel measure with σ -porous sets as null sets, Real Analysis Exchange 12 (1986-87), 349-353. (1986-87) Zbl0649.28005MR0873903
  7. Šleich P., Sets of type H ( s ) are σ -bilaterally porous, unpublished. 
  8. Zajíček L., Sets of σ -porosity and sets of σ -porosity(q), Časopis Pěst. Mat. 101 (1976), 350-359. (1976) Zbl0341.30026MR0457731
  9. Zajíček L., Porosity and σ -porosity, Real Analysis Exchange 13 (1987-88), 314-350. (1987-88) MR0943561
  10. Zajíček L., A note on σ -porous sets, Real Analysis Exchange 17.1 (1991-92), 18. (1991-92) 

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