Illinois Journal of Mathematics

Uniqueness in ergodic decomposition of invariant probabilities

Dieter Zimmermann

Full-text: Open access

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


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