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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Abstract

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

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

Dates
First available: 18 June 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1024404418

Mathematical Reviews number (MathSciNet)
MR1434125

Digital Object Identifier
doi:10.1214/aop/1024404418

Zentralblatt MATH identifier
0878.60006

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

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

Citation

Bélisle, Claude; Massé, Jean-Claude; Ransford, Thomas. When is a probability measure determined by infinitely many projections?. The Annals of Probability 25 (1997), no. 2, 767--786. doi:10.1214/aop/1024404418. http://projecteuclid.org/euclid.aop/1024404418.


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References

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