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2009•Journal of Shandong UniversityRequires access

Generalized Egoroff theorems of sequence of fuzzy valued functions

Yanhong Li

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Abstract

On the general fuzzy measure space,aiming at the sequence of measurable fuzzy valued functions,we present the concepts of almost everywhere convergence(or pseudo-almost everywhere convergence)and almost uniform convergence(or pseudo-almost uniform convergence),study the implication relationship of almost everywhere convergence and pseudo-almost everywhere convergence or almost uniform convergence and pseudo-almost uniform convergence.Thereby many different kinds of fuzzy generalized Egoroff theorems are obtained.

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What this paper is about

On the general fuzzy measure space,aiming at the sequence of measurable fuzzy valued functions,we present the concepts of almost everywhere convergence(or pseudo-almost everywhere convergence)and almost uniform convergence(or pseudo-almost uniform convergence),study the implication relationship of almost everywhere convergence and pseudo-almost everywhere convergence or almost uniform convergence and pseudo-almost uniform convergence.Thereby many different kinds of fuzzy generalized Egoroff theorems are obtained.

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Available abstract

On the general fuzzy measure space,aiming at the sequence of measurable fuzzy valued functions,we present the concepts of almost everywhere convergence(or pseudo-almost everywhere convergence)and almost uniform convergence(or pseudo-almost uniform convergence),study the implication relationship of almost everywhere convergence and pseudo-almost everywhere convergence or almost uniform convergence and pseudo-almost uniform convergence.Thereby many different kinds of fuzzy generalized Egoroff theorems are obtained.

Key concepts: Almost everywhere, Dominated convergence theorem, Convergence (economics), Compact convergence, Normal convergence, Modes of convergence (annotated index), Mathematics, Sequence (biology)

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