关于 Sierpiński 的两个定理
一般拓扑
2018-04-10 v5
摘要
Sierpiński 的一个定理指出，每个实数无穷集 Q 都包含无限多个不相交的子集，这些子集的外 Lebesgue 测度与 Q 的相同。他还有一个涉及 Baire 性质的类似定理。我们给出了一个此类的一般性定理及其推论，加强了经典结果。
引用
@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}
}
备注
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