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\input zb-ioport
\iteman{io-port 00046814}
\itemau{Zimmermann, Dieter}
\itemti{\"Uber die Integraldarstellung stochastischer Felder. Unter Verwendung von Methoden der Nonstandard-Analysis. (On the integral representation of stochastic fields. With use of nonstandard analysis methods).}
\itemso{Kaiserslautern: Universit\"at, FB Math., Diss. iv, 114 S. (1990).}
\itemab
In this dissertation the author proves the following uniqueness theorem for ergodic decompositions. Let T be a family of transition kernels on a measurable space (X,${\cal B})$. Let $\mu$ be a T-invariant probability and let E denote the set of all ergodic (i.e. extremal) T-invariant probabilities. Then there is at most one probability measure p over E such that $\mu (B)=\int\sb{E}v(B)dp(v)$ for all $B\in {\cal B}.$ All previous results in this direction needed additional assumptions on X and T. The method is a nontrivial nonstandard analysis version of arguments of {\it J. Kerstan} and {\it A. Wakolbinger}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 399-414 (1981; Zbl 0444.60004).
\itemrv{H.v.Weizs\"acker}
\itemcc{}
\itemut{ergodic decomposition; nonstandard analysis; Gibbs measures}
\itemli{}
\end