## The Annals of Probability

- Ann. Probab.
- Volume 1, Number 4 (1973), 716-718.

### A Note on the Convergence of Stable and Class L Probability Measures on Banach Spaces

#### Abstract

It is proved that the class of stable probability measures and the class of self-decomposible probability measures on Banach spaces are closed under weak convergence.

#### Article information

**Source**

Ann. Probab., Volume 1, Number 4 (1973), 716-718.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996900

**Digital Object Identifier**

doi:10.1214/aop/1176996900

**Mathematical Reviews number (MathSciNet)**

MR415707

**Zentralblatt MATH identifier**

0263.60001

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B05: Probability measures on topological spaces

Secondary: 60B10: Convergence of probability measures

**Keywords**

Infinitely divisible probability measure stable probability measure self-decomposible probability measure compact convegence types theorem weak convergence

#### Citation

Kumar, A. A Note on the Convergence of Stable and Class L Probability Measures on Banach Spaces. Ann. Probab. 1 (1973), no. 4, 716--718. doi:10.1214/aop/1176996900. https://projecteuclid.org/euclid.aop/1176996900