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Martin's axiom and Hausdorif measures

Published online by Cambridge University Press:  24 October 2008

A. J. Ostaszewski
A. J. Ostaszewski
Affiliation:
Mathematics Department, University College London, Gower Street, London WC1E 6BT
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Abstract

A theorem of Besicovitch, namely that, assuming the continuum hypothesis, there exists in any uncountable complete separable metric space a set of cardinality the continuum all of whose Hausdorif h-measures are zero, is here deduced by appeal to Martin's Axiom. It is also shown that for measures λ of Hausdorff type the union of fewer than 2ℵ0 sets of λ-measure zero is also of λ-measure zero; furthermore, the union of fewer than 2ℵ0 λ-measurable sets is λ-measurable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 193 - 197
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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