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Decomposition of Functions of Bounded Variation

Gary L. Grunkemeier
The Annals of Probability
Vol. 3, No. 2 (Apr., 1975), pp. 329-337
Stable URL: http://www.jstor.org/stable/2959396
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Decomposition of Functions of Bounded Variation
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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.

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