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Martin's axiom and Hausdorif measures
Published online by Cambridge University Press: 24 October 2008
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.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 193 - 197
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- Copyright © Cambridge Philosophical Society 1974
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