On a theorem of Banach and Kuratowski and K-Lusin sets
by
Lorenz Halbeisen
Queen's University Belfast
Coauthors: Tomek Bartoszynski

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 reals 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 not CH.

Paper reference: arXiv:math.LO/0107165

Date received: March 11, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagb-09.