ON SETS NONMEASURABLE WITH RESPECT TO INVARIANT-MEASURES

被引：6

作者：

SOLECKI, S ^{[1
]}

机构：

[1] UNIV WROCLAW,INST MATH,PL-50384 WROCLAW,POLAND

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 119卷 / 01期

关键词：

INVARIANT MEASURES; NONMEASURABLE SETS; EXTENSIONS OF MEASURES;

D O I：

10.2307/2159832

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A group G acts on a set X, and mu is a G-invariant measure on X. Under certain assumptions on the action of G and on mu (e.g., G acts freely and is uncountable, and mu is sigma-finite), we prove that each set of positive mu-measure contains a subset nonmeasurable with respect to any invariant extensions of mu. We study the case of ergodic measures in greater detail.

引用

页码：115 / 124

页数：10

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