## The Annals of Probability

- Ann. Probab.
- Volume 2, Number 1 (1974), 163-166.

### Nearest Random Variables with Given Distributions

#### Abstract

A new proof, based on the duality theorem of linear programming, is given of a theorem of V. Strassen, which states essentially that the minimum distance between random variables with given distributions equals the Prokhorov distance of their distributions.

#### Article information

**Source**

Ann. Probab., Volume 2, Number 1 (1974), 163-166.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996763

**Digital Object Identifier**

doi:10.1214/aop/1176996763

**Mathematical Reviews number (MathSciNet)**

MR353396

**Zentralblatt MATH identifier**

0292.60011

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B10: Convergence of probability measures

Secondary: 60B99: None of the above, but in this section

**Keywords**

Prokhorov distance Ky Fan distance minimum distance between random variables duality theorem of linear programming

#### Citation

Schay, Geza. Nearest Random Variables with Given Distributions. Ann. Probab. 2 (1974), no. 1, 163--166. doi:10.1214/aop/1176996763. https://projecteuclid.org/euclid.aop/1176996763