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2008•Unpublished venueRequires access

The nonstandard characterization of uniformly integrable functions

Shi Yan-wei

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Abstract

Let(X,A,u)be a finite internal finitely additive measure space.Firstly,some equivalent conditions of S-integrable are proved.Then we show the nonstandard characterization of uniformly integrable functions. Let {f_i}_(i∈I)be a collection of measurable functions.Then {fi}_(i∈I)is uniformly integrable if and only if f_i is S-integrable for each i∈~*I.

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Let(X,A,u)be a finite internal finitely additive measure space.Firstly,some equivalent conditions of S-integrable are proved.Then we show the nonstandard characterization of uniformly integrable functions. Let {f_i}_(i∈I)be a collection of measurable functions.Then {fi}_(i∈I)is uniformly integrable if and only if f_i is S-integrable for each i∈~*I.

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Available abstract

Let(X,A,u)be a finite internal finitely additive measure space.Firstly,some equivalent conditions of S-integrable are proved.Then we show the nonstandard characterization of uniformly integrable functions. Let {f_i}_(i∈I)be a collection of measurable functions.Then {fi}_(i∈I)is uniformly integrable if and only if f_i is S-integrable for each i∈~*I.

Key concepts: Integrable system, Mathematics, Locally integrable function, Characterization (materials science), Pure mathematics, Space (punctuation), Measure (data warehouse), Mathematical analysis

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