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

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

2001-07-23

arxiv.org/abs/math/0107165v1

Mathematics

Logic

Scientific paper

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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