Sets of filter convergence of sequences of continuous functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Reclaw, Ireneusz

关键词: Filter convergence;    Borel hierarchy;    Sequences of continuous functions;   

DOI  :  10.1016/j.jmaa.2012.05.030

来源: Elsevier

【 摘 要 】

We consider sets of filter convergence and divergence to infinity of sequences of continuous functions for Borel filters. We characterize the sets of filter convergence of sequences of continuous functions on the real line for Borel filters. We also give sufficient and necessary conditions for results involving sets of filter divergence to infinity. In particular, we give the full description of such sets for the statistical convergence for metric spaces. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free