Abstract

The aim of this paper is to define two sorts of convergence in measure, that is, outer and inner statistical convergence, for double sequences of fuzzy-valued measurable functions and demonstrate that both kinds of convergence are equivalent in a finite measurable set. We also define the notion of statistical convergence in measure for double sequences of fuzzy-valued measurable functions and establish several interesting results. In addition, we prove the statistical version of Egorov’s theorem for double sequences of fuzzy-valued functions defined on a finite measure space.

中文翻译：

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模糊值函数双序列的度量统计收敛

摘要

本文的目的是为模糊值可测函数的双序列定义度量的两种收敛，即外部和内部统计收敛，并证明这两种收敛在有限的可测集合中是等效的。我们还定义了统计收敛性的概念，用于度量模糊值可测量函数的双序列，并建立了一些有趣的结果。此外，我们证明了在有限度量空间上定义的模糊值函数的双序列的Egorov定理的统计形式。