Asian Research Journal of Mathematics

Extensions of the Lusin's Theorem, the Severini-Egorov's Theorem and the Riesz Subsequence Theorems

Mangatiana A. Robdera *

Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.

*Author to whom correspondence should be addressed.

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Abstract

We give extensions of the Lusin's Theorem, the Severini-Egorov's Theorem, and the Riesz Subsequence Theorems to the setting of a non-additive vector valued set functions and sequences of functions taking values in general metric spaces.

Keywords: Convergence theorems, Lusin's theorem, Severini-Egorov's theorem, Borel Cantelli's Lemma, Riesz subsequence theorems, vector valued set functions

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