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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 ameasurable 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; thisholds, for example, if μ∗ is the outer measure induced by ameasure which is σ- finite on X [2, theorem C, p. 50].

Information

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