Weak and point-wise convergence in C(K) for filter convergence

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:350

Article

Kadets, Vladimir¹  Leonov, Alexander¹ 

[1] Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine

关键词: Measurable functions;    Filter convergence;    Dominated convergence theorem for filters;    Extremal lest for weak convergence;    Banach space;   

DOI  :  10.1016/j.jmaa.2008.01.007

来源: Elsevier

【 摘 要 】

We study those filters F on N for which weak F-convergence of bounded sequences in C(K) is equivalent to point-wise F-convergence. We show that it is sufficient to require this property only for C[0, 1] and that the filter-analogue of the Rainwater extremal test theorem arises from it. There are ultrafilters which do not have this property and under the continuum hypothesis there are ultrafilters which have it. This implies that the validity of the Lebesgue dominated convergence theorem for F-convergence is more restrictive than the property which we study. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free