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An Extension Theorem Concerning Frechet Measures

Published online by Cambridge University Press:  20 November 2018

Ron C. Blei
Ron C. Blei*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
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Abstract

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An F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.

Keywords

28A3546E2726D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 278 - 285
Copyright
Copyright © Canadian Mathematical Society 1995

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