## Statistical Science

- Statist. Sci.
- Volume 1, Number 1 (1986), 78-91.

### The Central Limit Theorem Around 1935

#### Abstract

A long standing problem of probability theory has been to find necessary and sufficient conditions for the approximation of laws of sums of random variables by Gaussian distributions. A chapter in that search was closed by the 1935 work of Feller and Levy and by a beautiful result of Cramer published in early 1936. We review the respective contributions of Feller and Levy mentioning as necessary contributions of Laplace, Poisson, Lindeberg, Bernstein, Kolmogorov, and others, with an effort to place them in the context of the authors' times and in a modern content.

#### Article information

**Source**

Statist. Sci. Volume 1, Number 1 (1986), 78-91.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1177013818

**Digital Object Identifier**

doi:10.1214/ss/1177013818

**Mathematical Reviews number (MathSciNet)**

MR833276

**Zentralblatt MATH identifier**

0603.60001

**JSTOR**

links.jstor.org

**Keywords**

Central Limit Theorem Gaussian distributions characteristic functions martingales

#### Citation

Cam, L. Le. The Central Limit Theorem Around 1935. Statist. Sci. 1 (1986), no. 1, 78--91. doi:10.1214/ss/1177013818. https://projecteuclid.org/euclid.ss/1177013818

#### See also

- See Comment: H. F. Trotter. [The Central Limit Theorem Around 1935]: Comment. Statist. Sci., Volume 1, Number 1 (1986), 92--93.Project Euclid: euclid.ss/1177013819
- See Comment: J. L. Doob. [The Central Limit Theorem Around 1935]: Comment. Statist. Sci., Volume 1, Number 1 (1986), 93--94.Project Euclid: euclid.ss/1177013820
- See Comment: David Pollard. [The Central Limit Theorem Around 1935]: Comment. Statist. Sci., Volume 1, Number 1 (1986), 94--95.Project Euclid: euclid.ss/1177013821
- See Comment: L. Le Cam. [The Central Limit Theorem Around 1935]: Rejoinder. Statist. Sci., Volume 1, Number 1 (1986), 95--96.Project Euclid: euclid.ss/1177013822