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Keywords:
permitted trigonometric thin sets; set of perfect measure zero; set of uniform measure zero; s-set
permitted trigonometric thin sets; set of perfect measure zero; set of uniform measure zero; s-set
Summary:
We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions.
References:
[1] Arbault M.J.: Sur l'ensemble de convergence absolue d'une série trigonométrique. Bull. Soc. Math. France 80 (1952), 253-317. MR 0055476 | Zbl 0048.04202
[2] Bartoszyński T., Recław I.: Not every $\gamma$-set is strongly meager. Set theory (Bartoszynski T. et al., eds.). Annual Boise extravaganza in set theory conference, 1992/1994, Boise State University, Boise, ID, USA Contemp. Math. 192 (1996), 25-29. MR 1367132
[3] Bartoszyński T., Scheepers M.: Remarks on sets related to trigonometric series. Topology Appl. 64 (1995), 133-140. MR 1340865
[4] Bary N.K.: azbuka Trigonometricheskie ryady. Moskva (1961), English translation A Treatise on Trigonometric Series Macmillan New York (1964). MR 0171116
[5] Bukovská Z.: Thin sets in trigonometrical series and quasinormal convergence. Math. Slovaca 40 (1990), 53-62. MR 1094972
[6] Bukovská Z.: Thin sets defined by a sequence of continuous functions. Math. Slovaca 49 (1999), 3 323-344. MR 1728243
[7] Bukovská Z., Bukovský L.: Adding small sets to an N-set. Proc. Amer. Math. Soc. 123 (1995), 1367-1373. MR 1285977
[8] Bukovský L.: Thin sets in a general setting. Tatra Mountains Mathematical Publications 14 (1998), 241-260. MR 1651217
[9] Bukovský L., Kholshchevnikova N.N., Repický M.: Thin sets of harmonic analysis and infinite combinatorics. Real Anal. Exchange 20 (1994/95), 454-509. MR 1348075
[10] Bukovský L., Recław I., Repický M.: Spaces not distinguishing convergence of real-valued functions. Topology Appl. 112 (2001), 13-40.
[11] Galvin F., Miller A.W.: $\gamma$-sets and other singular sets of real numbers. Topology Appl. 17 (1984), 145-155. MR 0738943 | Zbl 0551.54001
[12] Just W., Miller A.W., Scheepers M., Szeptycki P.J.: The combinatorics of open covers, II. Topology Appl. 73 (1996), 3 241-266. MR 1419798 | Zbl 0870.03021
[13] Kada M., Kamo S.: New cardinal invariants related to pseudo-Dirichlet sets. preprint, 1996.
[14] Kahane S.: Antistable classes of thin sets in harmonic analysis. Illinois J. Math. 37 (1993), 2 186-223. MR 1208819 | Zbl 0793.42003
[15] Kholshchevnikova N.N.: Uncountable R- and N-sets. Math. Notes 38 (1985), 847-851. MR 0808896
[16] Kholshchevnikova N.N.: azbuka Primenenie teoretiko-mnozhestvennykh metodov v teorii ryadov. PhD Thesis Ross. Akad. Nauk Mat. Inst. (V. A. Steklov), Moskva (1993).
[17] Laflamme C.: Combinatorial aspects of $F_\sigma$ filters with an application to N-sets. Proc. Amer. Math. Soc. 125 (1997), 10 3019-3025. MR 1401747
[18] Miller A.W.: Some properties of measure and category. Trans. Amer. Math. Soc. 226 (1981), 93-144. MR 0613787 | Zbl 0472.03040
[19] Repický M.: A family of permitted trigonometric thin sets. Proc. Amer. Math. Soc. 125 (1997), 1 137-144. MR 1343721
[20] Repický M.: Towers and permitted trigonometric thin sets. Real Anal. Exchange 21 (1995/96), 648-655. MR 1407277
[21] Repický M.: Mycielski ideal and the perfect set theorem. preprint, 2001. MR 2053988
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