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On the Selection of Compact Subsets of Positive Measure from Analytic Sets of Positive Measure
Published online by Cambridge University Press: 20 November 2018
Extract
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 1974
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