Measurable Cover Functions
- 1 October 1967
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 10 (4) , 519-523
- https://doi.org/10.4153/cmb-1967-051-4
Abstract
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].Keywords
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