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 L-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∞（Iμ）.We also show that the usual sequential convergence is not equivalent to a single measure convergence.