Geodesic
Measurable Cover Functions
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 519-523

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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]. 
Eames, W.; May, L. E. Measurable Cover Functions. Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 519-523. doi: 10.4153/CMB-1967-051-4
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     title = {Measurable {Cover} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {519--523},
     year = {1967},
     volume = {10},
     number = {4},
     doi = {10.4153/CMB-1967-051-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-051-4/}
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