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.
Publié le : 1976-06-14
Classification:
Admissible translates,
probability measure,
absolute continuity,
positive density,
support of a probability distribution,
28A10,
60E05
@article{1176996103,
author = {Hudson, William N.},
title = {Admissible Translates for Probability Distributions},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 505-508},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996103}
}
Hudson, William N. Admissible Translates for Probability Distributions. Ann. Probab., Tome 4 (1976) no. 6, pp. 505-508. http://gdmltest.u-ga.fr/item/1176996103/