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June, 1976 Admissible Translates for Probability Distributions
William N. Hudson
Ann. Probab. 4(3): 505-508 (June, 1976). DOI: 10.1214/aop/1176996103


A real number $t$ is an admissible translate of a probability $\varphi$ if $\varphi (A) = 0$ implies that $\varphi_t(A) \equiv \varphi (A - t) = 0$. Conditions are given on its set of admissible translates which ensure that $\varphi$ has a density. The theorems also describe the set where the density is positive and contain as a corollary the result that if $\varphi$ is not absolutely continuous, then the set of admissible translates has an empty interior.


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William N. Hudson. "Admissible Translates for Probability Distributions." Ann. Probab. 4 (3) 505 - 508, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0336.60015
MathSciNet: MR426094
Digital Object Identifier: 10.1214/aop/1176996103

Primary: 28A10
Secondary: 60E05

Keywords: Absolute continuity , Admissible translates , positive density , probability measure , support of a probability distribution

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
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