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Measurable envelopes, Hausdorff measures and Sierpiński sets

Márton Elekes (2003)

Colloquium Mathematicae

We show that the existence of measurable envelopes of all subsets of ℝⁿ with respect to the d-dimensional Hausdorff measure (0 < d < n) is independent of ZFC. We also investigate the consistency of the existence of d -measurable Sierpiński sets.

Measures on Corson compact spaces

Kenneth Kunen, Jan van Mill (1995)

Fundamenta Mathematicae

We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.

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