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arXiv · 1709.09607

On two theorems of Sierpi\'nski

Edward Grzegorek·Iwo Labuda
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Abstract

A theorem of Sierpi\'nski says that every infinite set Q of reals contains an infinite number of disjoint subsets whose outer Lebesgue measure is the same as that of Q. He also has a similar theorem involving the Baire property. We give a general theorem of this type and its corollaries, strengthening classical results.

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Edward Grzegorek, Iwo Labuda. 2017-09-27. On two theorems of Sierpi\'nski. https://arxiv.org/abs/1709.09607

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