Statistical convergence and ideal convergence for sequences of functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:328

Article

Balcerzak, Marek ; Dems, Katarzyna ; Komisarski, Andrzej

关键词: I-uniform convergence;    equi-statistical convergence;    statistical Egorov's theorem;    statistical convergence in measure;   

DOI  :  10.1016/j.jmaa.2006.05.040

来源: Elsevier

【 摘 要 】

Let I subset of P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X, M, mu), we obtain a statistical version of the Egorov theorem (when mu(X) < infinity). We show that, in its assertion, equi-statistical convergence on a big set cannot be replaced by uniform statistical convergence. Also, we consider statistical convergence in measure and I-convergence in measure, with some consequences of the Riesz theorem. We prove that outer and inner statistical convergences in measure (for sequences of measurable functions) are equivalent if the measure is finite. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free