拓扑群上的拟不变测度与ω-幂

IF 0.8 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal Pub Date : 2023-10-04 DOI:10.1515/gmj-2023-2073

Alexander Kharazishvili

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引用次数: 0

摘要

在GCH下，描述了所有Hausdorff拓扑群G的基数，使得G上存在一个非零Borel测度，该测度具有card (G) {{\rm card}(G)} -Suslin性质，并且对于G的处处稠密子群具有拟不变量。利用Kodaira和Kakutani(1950)的方法构造标准Lebesgue (Haar)测度在圆群上的不可分平移不变扩展，指出了一些联系。

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Quasi-invariant measures on topological groups and ω-powers

Abstract Under GCH , there are described the cardinalities of all Hausdorff topological groups G such that there is a nonzero Borel measure on G having the card ⁢ ( G ) {{\rm card}(G)} -Suslin property and quasi-invariant with respect to an everywhere dense subgroup of G . Some connections are pointed out with the method of Kodaira and Kakutani (1950) for constructing a nonseparable translation invariant extension of the standard Lebesgue (Haar) measure on the circle group 𝐒 1 {{\bf S}_{1}} .

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来源期刊

Georgian Mathematical Journal 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.