## The Annals of Probability

- Ann. Probab.
- Volume 14, Number 1 (1986), 336-342.

### Entropy and the Central Limit Theorem

#### Abstract

A strengthened central limit theorem for densities is established showing monotone convergence in the sense of relative entropy.

#### Article information

**Source**

Ann. Probab. Volume 14, Number 1 (1986), 336-342.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aop/1176992632

**Digital Object Identifier**

doi:10.1214/aop/1176992632

**Mathematical Reviews number (MathSciNet)**

MR815975

**Zentralblatt MATH identifier**

0599.60024

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 94A17: Measures of information, entropy 62B10: Information-theoretic topics [See also 94A17]

**Keywords**

Central limit theorem local limit theorem entropy Fisher information convolution inequalities

#### Citation

Barron, Andrew R. Entropy and the Central Limit Theorem. Ann. Probab. 14 (1986), no. 1, 336--342. doi:10.1214/aop/1176992632. http://projecteuclid.org/euclid.aop/1176992632.