Journal of the Ramanujan Mathematical Society

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Equi-Uniformly and Equi-Contiguous Integrable Functions


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1 Queen's University at Kingston, Ontario, Canada
     

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The concepts of contiguity, equi-uniformly integrable functions and equi-contiguous integrable functions are defined. The various properties of these concepts and their relations have been investigated. The necessary and sufficient conditions for equi-uniformly integrable functions are discussed, and sufficient conditions for equi-contiguous integrable functions are appended. Motivation for investigation of these concepts has been stated.

Keywords

Absolute Continuity, Contiguity, Equi-Contiguous Integrable Functions, Equi-Uniformly Integrable Functions, Sequence of Measures Spaces Summable Functions.
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  • Equi-Uniformly and Equi-Contiguous Integrable Functions

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Authors

M. T. Wasan
Queen's University at Kingston, Ontario, Canada

Abstract


The concepts of contiguity, equi-uniformly integrable functions and equi-contiguous integrable functions are defined. The various properties of these concepts and their relations have been investigated. The necessary and sufficient conditions for equi-uniformly integrable functions are discussed, and sufficient conditions for equi-contiguous integrable functions are appended. Motivation for investigation of these concepts has been stated.

Keywords


Absolute Continuity, Contiguity, Equi-Contiguous Integrable Functions, Equi-Uniformly Integrable Functions, Sequence of Measures Spaces Summable Functions.