l-selection principles for sequences of functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Filipow, Rafal¹  Mrozek, Nikodem¹  Reclaw, Ireneusz²  Szuca, Piotr¹ 

[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

[2] Univ Gdansk, Inst Informat, PL-80952 Gdansk, Poland

关键词: Bolzano-Weierstrass property;    Ideal convergence;    Selection principle;    Bounded function sequence;    Arzela-Ascoli theorem;    Helly's theorem;    Mazurkiewicz's theorem;   

DOI  :  10.1016/j.jmaa.2012.06.050

来源: Elsevier

【 摘 要 】

We generalize three classical selection principles (Arzela-Ascoli theorem, Mazurkiewicz's theorem and Helly's theorem) on the ideal convergence. In particular, we show that for every analytic P-ideal l with the BW property (and every Fa ideal 1) the following selection theorems hold: If < f(n)>(n) is a sequence of uniformly bounded equicontinuous functions on [0, 1] then there exists A is not an element of l such that < f(n)>(n epsilon A) is uniformly convergent; if < f(n)>(n) is a sequence of uniformly bounded continuous functions then there exists a perfect set P and a set A is not an element of l such that < f(n) vertical bar P >(n epsilon A) is pointwise convergent; if < f(n)>(n) is a sequence of uniformly bounded monotone functions then there exists a set A is not an element of l such that < f(n)>(n epsilon A) is pointwise convergent. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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