On the generalized nonmeasurability of Vitali sets and Bernstein sets

被引：0
|
作者：
Kharazishvili, Alexander [1 ]
机构：
[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, 6 Tamarashvili Str, GE-0177 Tbilisi, Georgia
来源：
GEORGIAN MATHEMATICAL JOURNAL | 2021年 / 28卷 / 04期
基金：
美国国家科学基金会;
关键词：
Real-valued measurable cardinal; Vitali set; Bernstein set; selector; continuum hypothesis;
D O I：
10.1515/gmj-2020-2083
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that the cardinality of the continuum is not real-valued measurable if and only if there exists no nonzero sigma-finite diffused measure mu on the real line such that all Vitali sets (respectively all Bernstein sets) are mu-measurable.
引用
收藏
页码：575 / 579
页数：5
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