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Measurable Cover Functions
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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].
Title: Measurable Cover Functions
Description:
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].
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