O. Duman, Ankara University, Faculty of Science, Dept. of Mathematics, Tandogan 06100, Ankara, Turkey, e-mail: oduman@science.ankara.edu.tr; C. Orhan, Ankara University, Faculty of Science, Dept. of Mathematics, Tandogan 06100, Ankara, Turkey, orhan@science.ankara.edu.tr
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
Classification (MSC 2000): 40A30
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