## Illinois Journal of Mathematics

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

### Uniqueness in ergodic decomposition of invariant probabilities

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/ijm/1255987540

**Mathematical Reviews number (MathSciNet)**

MR1156633

**Zentralblatt MATH identifier**

0741.46003

**Subjects**

Primary: 28E05: Nonstandard measure theory [See also 03H05, 26E35]

Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 46S20: Nonstandard functional analysis [See also 03H05]

#### 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