Cramer's theorem, that a normal distribution function $(\operatorname{df})$ has only normal components, is extended to a case where the components are allowed to be from a subclass $(B_1)$ of the functions of bounded variation other than the class of df's. One feature of $B_1$ is that it contains more of the df's than the classes for which previous similar extensions have been made; in particular it contains the Poisson df's so that a first extension of Raikov's theorem, that a Poisson df has only Poisson components, in the same direction, is also given.
@article{1176996403,
author = {Grunkemeier, Gary L.},
title = {Decomposition of Functions of Bounded Variation},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 329-337},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996403}
}
Grunkemeier, Gary L. Decomposition of Functions of Bounded Variation. Ann. Probab., Tome 3 (1975) no. 6, pp. 329-337. http://gdmltest.u-ga.fr/item/1176996403/