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December, 1975 A Note on the Proof of the Zero-One Law of Blum and Pathak
Wolfgang Sendler
Ann. Probab. 3(6): 1055-1058 (December, 1975). DOI: 10.1214/aop/1176996234

Abstract

Let $\{(\Omega, \mathscr{A}, \mu_n), n \geqq 1\}$ be a sequence of probability spaces. Blum and Pathak [Ann. Math. Statist. 43 (1972) 1008-1009] proved a zero-one law for permutation invariant sets $A \epsilon \mathscr{A}^\infty$; which includes the zero-one laws of Hewitt and Savage [Trans. Amer. Math. Soc. 80 (1955) 470-501] and Horn and Schach [Ann. Math. Statist. 41 (1970) 2130-2131] as special cases. The proper reason for this is shown to be the fact that the set of measures admitting the zero-one law of Blum and Pathak coincides with the set of all strong limit points of measures admitting the zero-one law of Horn and Schach.

Citation

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Wolfgang Sendler. "A Note on the Proof of the Zero-One Law of Blum and Pathak." Ann. Probab. 3 (6) 1055 - 1058, December, 1975. https://doi.org/10.1214/aop/1176996234

Information

Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0329.60015
MathSciNet: MR380953
Digital Object Identifier: 10.1214/aop/1176996234

Subjects:
Primary: 60F20

Keywords: Hewitt-Savage zero-one law , Horn-Schach zero-one law

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • December, 1975
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