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Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.
5
votes
Accepted
Subsets $X$ such that their Hausdorff outer measure is not finite
Yes, if $X$ is an analytic set. See:
Besicovitch, On existence of subsets of finite measure of sets of infinite measure, 1952
R. O. Davies, Subsets of finite measure in analytic sets, 1951.
For di …