关于Borel集的一个注记  

A Note on the Borel Set

作　　者：林梅羽[1] 

机构地区：[1]莆田学院基础教育学院,福建莆田351100

出　　处：《莆田学院学报》2015年第5期8-10,68,共4页Journal of putian University

摘　　要：从教科书中关于Borel集定义的两种不同叙述法入手,应用超限归纳法,证明了这两种定义的等价性,并根据基数理论,证明了非Borel的Lebesgue可测集的存在性,进而证明了R1上非Borel的Lebesgue可测集的基数是2c-c,其中c为连续统基数。Two different statements of Borel set of R1 were referred in textbooks. Transfinite induction was used in this paper to prove the equivalence of the two different statements. Based on Z-F Axiom Systems of set theory,the paper proved the existence of the measurable set of non-Borel of Lebesgue. Furthermore, it showed that the measurable set of non-Borel of Lebesgue on R1 was 2c- c, and c is the cardinal number of continuum.

关 键 词：BOREL集 超限归纳法 基数理论 Lebesgue可测集 

分 类 号：O174.1[理学—数学]