$\mu$-statistically convergent function sequences

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