abstract
On a theorem of Banach and Kuratowski and K-Lusin sets
Tomek Bartoszynski and Lorenz Halbeisen
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.