## Illinois Journal of Mathematics

### Uniqueness in ergodic decomposition of invariant probabilities

Dieter Zimmermann

#### Abstract

We show that for any set of transition probabilities on a common measurable space and any invariant probability, there is at most one representing measure on the set of extremal, invariant probabilities with the $\sigma$-algebra generated by the evaluations. The proof uses nonstandard analysis.

#### Article information

Source
Illinois J. Math., Volume 36, Issue 2 (1992), 325-344.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.ijm/1255987540

Digital Object Identifier
doi:10.1215/ijm/1255987540

Mathematical Reviews number (MathSciNet)
MR1156633

Zentralblatt MATH identifier
0741.46003

#### Citation

Zimmermann, Dieter. Uniqueness in ergodic decomposition of invariant probabilities. Illinois J. Math. 36 (1992), no. 2, 325--344. doi:10.1215/ijm/1255987540. https://projecteuclid.org/euclid.ijm/1255987540