mu-Statistically Convergent Function Sequences

Authors: O. Duman1; C. Orhan2

Source: Czechoslovak Mathematical Journal, Volume 54, Number 2, June 2004 , pp. 413-422(10)

Publisher: Springer

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Abstract:

In the present paper we are concerned with convergence in mu-density and mu-statistical convergence of sequences of functions defined on a subset D of real numbers, where mu is a finitely additive measure. Particularly, we introduce the concepts of mu-statistical uniform convergence and mu-statistical pointwise convergence, and observe that mu-statistical uniform convergence inherits the basic properties of uniform convergence.

Keywords: pointwise and uniform convergence; mu-statistical convergence; convergence in mu-density; finitely additive measure; additive property for null sets

Document Type: Research article

DOI: 10.1023/B:CMAJ.0000042380.31622.39

Affiliations: 1: Ankara University, Faculty of Science, Dept. of Mathematics, Tandogbrevean 06100, Ankara, Turkey, Email: oduman@science.ankara.edu.tr an 06100, Ankara, Turkey, Email: oduman@science.ankara.edu.tr "> 2: Ankara University, Faculty of Science, Dept. of Mathematics, Tandogbrevean 06100, Ankara, Turkey, Email: orhan@science.ankara.edu.tran 06100, Ankara, Turkey, Email: orhan@science.ankara.edu.tr">

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