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An Elementary Result on Exponential Measure Spaces

Published online by Cambridge University Press:  20 November 2018

C. Y. Shen
C. Y. Shen*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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A simple but useful result in the measure theory for product spaces can be stated as follows:

Theorem A. A necessary and sufficient condition that a measurable subset E of X×Y has measure zero is that almost every X-section (or almost every Y-section) has measure zero (see [1, §36]).

We will show, in this short note, that a similar result also holds for the exponential of measure spaces. Before proceeding any further, we describe briefly here the exponential construction of a measure space.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 277 - 278
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Halmos, P. R., Measure theory, Van Nostrand, Princeton, N.J., 1950.Google Scholar
2. Carter, D. S. and Prenter, P. M., Exponential spaces and counting processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete (to appear).Google Scholar
3. Carter, D. S., The exponential of a measure space, Tech. Rep. No. 29, Dept. of Math., Oregon State Univ., Corvallis, 1966.Google Scholar