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Some Applications of a Theorem of Marcinkiewicz

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen  and
R. Vyborny
P. S. Bullen
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada
R. Vyborny
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland, Australia
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Abstract

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A classical theorem of Marcinkiewicz states that a function is Perron integrable iff it has one continuous major and one continuous minor function. Using an elaboration of this remarkable theorem three applications are made; to obtain a new proof of a recent characterization of the Perron integral, to proofs of some theorems on interchange of limits and integration and to extend classical existence theorems for ordinary differential equations.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 165 - 174
Copyright
Copyright © Canadian Mathematical Society 1991

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