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Absolutely non-measurable and singular co-analytic set

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

A. J. Ostaszewski
A. J. Ostaszewski
Affiliation:
Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE
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Extract

Davies and Rogers [5] constructed a compact metric space Ω which is singular for a certain Hausdorff measure μh, in the sense that all subsets of Ω have μh-measure zero or infinity and μh(Ω) = ∞. (For a further study of this example see Boardman [3]). The interest lies in its extremely good descriptive character, which was lacking in the earlier examples given by Besicovitch [2] (a plane set singular for linear measure) and Choquet [4] (a plane set singular for any Hausdorff measure for which a segment has positive measure).

MSC classification

Secondary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 161 - 163
Copyright
Copyright © University College London 1975

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References

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