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Measurable Cover Functions

Published online by Cambridge University Press:  20 November 2018

W. Eames  and
L. E. May
W. Eames
Affiliation:
Sir John Cass College
L. E. May
Affiliation:
Sir John Cass College
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Let μ∗ be an outer measure on (X, S) with σ- algebra S and let μ* be the inner measure induced by μ∗. A set M is a measurable cover of a set A ⊆ X if A ⊆ M, M is measurable, and μ∗ (M-A) = 0. We assume that every subset of X has a measurable cover; this holds, for example, if μ∗ is the outer measure induced by a measure which is σ- finite on X [2, theorem C, p. 50].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 519 - 523
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Eames, W., A Local Property of Measurable Sets, Can. J. Mathematics, 12, (1966), 63Z-640.Google Scholar
2. Halmos, P. R., Measure Theory, New York, (1955).Google Scholar
3. May, L. E., Locally Measurable Sets and Functions, accepted for publication in the Proceedings of the London Mathematical Society.Google Scholar