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On the selection of non-σ-finite subsets

Published online by Cambridge University Press:  26 February 2010

D. G. Larman
D. G. Larman
Affiliation:
University College, London.
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Let A be a subset of a compact metric space Ω, and suppose that A has non-σ-finite h-measure, where h is some Hausdorff function. The following problem was suggested to me by Professor C. A. Rogers:

If A is analytic, is it possible to construct 2ℵodisjoint closed subsets of A which also have non-σ-finite h-measure?

At this level of generality the problem, like others which involve selection of subsets, appears to offer some difficulty. Here we prove two results which were motivated by it.

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Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 161 - 164
Copyright
Copyright © University College London 1967

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References

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