On two theorems of Sierpi\'nski
General Topology
2018-04-10 v5
Abstract
A theorem of Sierpi\'nski says that every infinite set Q of reals contains an infinite number of disjoint subsets whose outer Lebesgue measure is the same as that of Q. He also has a similar theorem involving the Baire property. We give a general theorem of this type and its corollaries, strengthening classical results.
Cite
@article{arxiv.1709.09607,
title = {On two theorems of Sierpi\'nski},
author = {Edward Grzegorek and Iwo Labuda},
journal= {arXiv preprint arXiv:1709.09607},
year = {2018}
}
Comments
In the 1st replacement Proposition 3.4, Corollary 3.5 and 3.6 have been added. In the 2nd replacement subsection 4.2 in the Appendix (= Section 4) has been added. Next, a few improvement in the presentation were done, reference [12] was added, and a correction in the proof of Proposition 4.1 was introduced. Presently, historical comments are slightly modified