## The Annals of Probability

- Ann. Probab.
- Volume 25, Number 2 (1997), 531-1010

### When is a probability measure determined by infinitely many projections?

Claude Bélisle,Jean-Claude Massé, and Thomas Ransford

#### 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.