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.