## The Annals of Probability

### Admissible Translates for Probability Distributions

William N. Hudson

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 505-508.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996103

Digital Object Identifier
doi:10.1214/aop/1176996103

Mathematical Reviews number (MathSciNet)
MR426094

Zentralblatt MATH identifier
0336.60015

JSTOR