Statistical convergence and measure convergence generated by a single statistical measure |
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Authors: | Li Xin Cheng Li Hua Lin Xian Geng Zhou |
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Affiliation: | 1.School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China;2.nstitute of Mathematical and Information Engineering, Sanming University, Sanming 365004, P. R. China;3.Department of Mathematics, Ningde Normal University, Ningde 352100, P. R. China |
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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 ∞(I μ ). We also show that the usual sequential convergence is not equivalent to a single measure convergence. |
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Keywords: | Statistical measure ultrafilter extreme points statistical convergence |
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