2014
DOI: 10.14321/realanalexch.39.2.0459
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On Partitions of the Real Line into Continuum Many Thick Subsets

Abstract: Three classical constructions of Lebesgue nonmeasurable sets on the real line R are envisaged from the point of view of the thickness of those sets. It is also shown, within ZF & DC theory, that the existence of a Lebesgue nonmeasurable subset of R implies the existence of a partition of R into continuum many thick sets.

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