Geodesic
On the Selection of Compact Subsets of Positive Measure from Analytic Sets of Positive Measure
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 665-677

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

An important but seemingly difficult problem is to decide whether or not an analytic set A of positive h-measure, for some continuous Hausdorff function h, contains a compact subset C of positive h-measure, in every complete separable metric space Ω.By extending some earlier work of R. O. Davies [1], M. Sion and D. Sjerve [8] proved that (i) the selection of the set C is always possible in a σ-compact metric space Ω. More recently Davies [2] has shown that it is always possible to select C (ii) when h(t) = ts, t ≧ 0, for some fixed positive number s, (iii) when Ω is finite dimensional in the sense of [4], (iv) when A has σ-finite h-measure, and (v) when Ω is an ultra metric space. 
Larman, D. G. On the Selection of Compact Subsets of Positive Measure from Analytic Sets of Positive Measure. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 665-677. doi: 10.4153/CJM-1974-063-1
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[7] 7. Sierpinski, W., Introduction to general topology (Toronto, 1934). Google Scholar

[8] 8. Sion, M. and Sjerve, D., Approximation properties of measures generated by continuous set functions, Mathematika 9 (1962), 145–56. Google Scholar

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