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