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
相关论文
共 50 条
  • [41] GENERALIZED CLOSURE OF SETS
    HAMMER, PC
    SOBCZYK, A
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (04) : 491 - 492
  • [42] GENERALIZED LUZIN SETS
    Ralowski, Robert
    Zeberski, Szymon
    HOUSTON JOURNAL OF MATHEMATICS, 2013, 39 (03): : 983 - 993
  • [43] Generalized Lefschetz Sets
    Mirosław Ślosarski
    Fixed Point Theory and Applications, 2011
  • [44] On generalized open sets
    Hussain, Sabir
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2018, 47 (06): : 1438 - 1446
  • [45] COMPARISON BETWEEN THIN SETS AND GENERALIZED AZARIN SETS
    ESSEN, M
    JACKSON, HL
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1975, 18 (03): : 335 - 346
  • [46] Generalized Probabilistic Rough Sets Characterized by Fuzzy Sets
    Qiu, Xu-Qin
    Wei, Li-Li
    PROCEEDINGS OF THE 2009 WRI GLOBAL CONGRESS ON INTELLIGENT SYSTEMS, VOL I, 2009, : 474 - 478
  • [47] SEMI GENERALIZED OPEN SETS AND GENERALIZED SEMI CLOSED SETS IN TOPOLOGICAL SPACES
    Hassan, Abdelgabar Adam
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2020, 18 (06): : 1029 - 1036
  • [48] Generalized ψρ-Closed Sets and Generalized ψρ-Open Sets in Double Fuzzy Topological Spaces
    Mohammed, Fatimah M.
    Noorani, M. S. M.
    Ghareeb, A.
    PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES, 2014, 1602 : 909 - 917
  • [49] Images of Bernstein sets via continuous functions
    Cichon, Jacek
    Morayne, Michal
    Ralowski, Robert
    GEORGIAN MATHEMATICAL JOURNAL, 2019, 26 (04) : 499 - 503
  • [50] A NEW ESTIMATE OF THE TRANSFINITE DIAMETER OF BERNSTEIN SETS
    Kenne, Dimitri Jordan
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2024, 27 (03): : 735 - 743
12345