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On Product of Radón Measures

Published online by Cambridge University Press:  20 November 2018

M. C. Godfrey  and
M. Sion
M. C. Godfrey
Affiliation:
University of British Columbia, Vancouver
M. Sion
Affiliation:
University of British Columbia, Vancouver
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Let X, Y be locally compact Hausdorff spaces and μ, ν be Radón outer measures on X and Y respectively. The classical product outer measure ϕ on X × Y generated by measurable rectangles, without direct reference to the topology, turns out to have some serious drawbacks. For example, one can only prove that closed sets (and hence Baire sets) are ϕ-measurable. It is unknown, even when X and Y are compact, whether closed sets are ϕ-measurable.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 427 - 444
Copyright
Copyright © Canadian Mathematical Society 1969

References

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