Decomposition of Functions of Bounded Variation

Abstract

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.