2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61890In 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.Logic03E35 (Primary) 03E17 03E05 (Secondary)text