## Annals of Probability

- Ann. Probab.
- Volume 8, Number 1 (1980), 142-147.

### A Conditional Law of Large Numbers

#### Abstract

It is shown that, when conditional on a set of given average values, the frequency distribution of a series of independent random variables with a common finite distribution converges in probability to the distribution which has the maximum relative entropy for the given mean values.

#### Article information

**Source**

Ann. Probab., Volume 8, Number 1 (1980), 142-147.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176994830

**Digital Object Identifier**

doi:10.1214/aop/1176994830

**Mathematical Reviews number (MathSciNet)**

MR556420

**Zentralblatt MATH identifier**

0426.60019

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60F99: None of the above, but in this section 82A05

**Keywords**

Limit theorems laws of large numbers conditional convergence entropy maximum entropy principle

#### Citation

Vasicek, Oldrich Alfonso. A Conditional Law of Large Numbers. Ann. Probab. 8 (1980), no. 1, 142--147. doi:10.1214/aop/1176994830. https://projecteuclid.org/euclid.aop/1176994830