Statistical convergence and measure convergence generated by a single statistical measure

The purpose of this paper is to discuss those kinds of statistical convergence, in terms of filter F, or ideal I-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l _∞/l _∞(I _μ ). We also show that the usual sequential convergence is not equivalent to a single measure convergence.