The Annals of Probability

When is a probability measure determined by infinitely many projections?

Claude Bélisle, Jean-Claude Massé, and Thomas Ransford

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The well-known Cramér-Wold theorem states that a Borel probability measure on $\mathbb{R}^d$ is uniquely determined by the totality of its one-dimensional projections. In this paper we examine various conditions under which a probability measure is determined by a subset of its $(d - 1)$-dimensional orthogonal projections.

Article information

Ann. Probab., Volume 25, Number 2 (1997), 767-786.

First available in Project Euclid: 18 June 2002

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Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 60E10: Characteristic functions; other transforms

Cramér-Wold theorem probability measure characteristic function projection analytic function quasi-analytic class determination


Bélisle, Claude; Massé, Jean-Claude; Ransford, Thomas. When is a probability measure determined by infinitely many projections?. Ann. Probab. 25 (1997), no. 2, 767--786. doi:10.1214/aop/1024404418.

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