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The Vitali Integral Convergence Theorem and Uniform Absolute Continuity

Published online by Cambridge University Press:  20 November 2018

Elizabeth M. Bator ,
Russell G. Bilyeu  and
Paul W. Lewis
Elizabeth M. Bator
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas, USA
Russell G. Bilyeu
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas, USA
Paul W. Lewis
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas, USA
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Abstract

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A geometric version of the Vitali integral convergence theorem is established. Parameterized versions of results on uniform absolute continuity in spaces of measures suggested by the convergence theorem are studied.

Keywords

46B2046A5028A3328A99Vitali integral convergence theoremuniform absolute continuityGateaux differentiability
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 939 - 947
Copyright
Copyright © Canadian Mathematical Society 1991

References

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