Open Access
October, 1978 Sufficient Statistics and Extreme Points
E. B. Dynkin
Ann. Probab. 6(5): 705-730 (October, 1978). DOI: 10.1214/aop/1176995424


A convex set $M$ is called a simplex if there exists a subset $M_e$ of $M$ such that every $P \in M$ is the barycentre of one and only one probability measure $\mu$ concentrated on $M_e$. Elements of $M_e$ are called extreme points of $M$. To prove that a set of functions or measures is a simplex, usually the Choquet theorem on extreme points of convex sets in linear topological spaces is cited. We prove a simpler theorem which is more convenient for many applications. Instead of topological considerations, this theorem makes use of the concept of sufficient statistics.


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E. B. Dynkin. "Sufficient Statistics and Extreme Points." Ann. Probab. 6 (5) 705 - 730, October, 1978.


Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0403.62009
MathSciNet: MR518321
Digital Object Identifier: 10.1214/aop/1176995424

Primary: 60J50
Secondary: 28A65 , 60K35 , 82A25

Keywords: 60-02 , entrance and exit laws , ergodic decomposition of an invariant measure , excessive measures and functions , extreme points , Gibbs states , sufficient statistics , symmetric measures

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 5 • October, 1978
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