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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Eames, W., A Local Property of Measurable Sets, Can. J. Mathematics, 12, (1966), 63Z-640. Google Scholar

[2] 2. Halmos, P. R., Measure Theory, New York, (1955). Google Scholar

[3] 3. May, L. E., Locally Measurable Sets and Functions, accepted for publication in the Proceedings of the London Mathematical Society. Google Scholar

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