Abstract
Let (Ω, ℱ, μ) be a perfect probability space with ℱ countably generated, and let IB be a family of sub-σ-fields of ℱ. Under a countability condition on the family IB, I show that there exists a family {π∇}∇∈IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the π∇ can furthermore be chosen to be everywhere proper. It follows that in the Dobrushin-Lanford-Ruelle formulation of the statistical mechanics of classical lattice systems, every (perfect) probability measure is a Gibbs measure for some specification.
Original language | English (US) |
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Pages (from-to) | 537-548 |
Number of pages | 12 |
Journal | Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete |
Volume | 56 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1981 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Mathematics(all)