On a theorem of Banach and Kuratowski and K-Lusin sets

Tomek Bartoszynski; Lorenz Halbeisen

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On a theorem of Banach and Kuratowski and K-Lusin sets

Tomek Bartoszynski·Lorenz Halbeisen

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Abstract

In a paper of 1929, Banach and Kuratowski proved, assuming the continuum hypothesis, a combinatorial theorem which implies that there is no non-vanishing sigma-additive finite measure on the real line which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size the continuum and that the existence of such sets is independent of ZFC plus non CH.

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BibTeX RIS

Tomek Bartoszynski, Lorenz Halbeisen. 2001-07-23. On a theorem of Banach and Kuratowski and K-Lusin sets. https://arxiv.org/abs/math/0107165

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