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