Thin sets in general setting

Rok, strany: 1998, 241 - 260

We introduce the notion of a family of thin sets, which includes the case of families of trigonometric thin sets. If a family is trigonometric like, then by the classical Steinhaus theorem all its members are meager and have measure zero. We investigate thin sets defined from sequence of continuous functions-the notion recently introduced by Z. Bukovská. Moreower, we show that such generalization of weak Dirichlet sets have almost all classical properties of weak Dirichlet sets. Some recent results by M. Repický, C. Laflamme, M. Kada and S. Kamo and others are generalized for so defined thin sets. Indeed we show that the estimates known for cardinal invariants of trigonometric thin sets are no better than those obtained for thin sets defined by a continuous function with suitable properties.

ISO 690:

Bukovský, L. 1998. Thin sets in general setting. In Tatra Mountains Mathematical Publications, vol. 14, no.1, pp. 241-260. 1210-3195.

APA:

Bukovský, L. (1998). Thin sets in general setting. Tatra Mountains Mathematical Publications, 14(1), 241-260. 1210-3195.