Abstract
A group G acts on a set X, and μ is a G-invariant measure on X. Under certain assumptions on the action of G and on μ (e.g., G acts freely and is uncountable, and μ is σ-finite), we prove that each set of positive μ-measure contains a subset nonmeasurable with respect to any invariant extensions of μ. We study the case of ergodic measures in greater detail.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 115-124 |
| Number of pages | 10 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 119 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 1993 |
| Externally published | Yes |
Keywords
- Extensions of measures
- Invariant measures
- Nonmeasurable sets
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics