On a theorem of Banach and Kuratowski and K-Lusin sets
Logic
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0107165,
title = {On a theorem of Banach and Kuratowski and K-Lusin sets},
author = {Tomek Bartoszynski and Lorenz Halbeisen},
journal= {arXiv preprint arXiv:math/0107165},
year = {2007}
}