## The Annals of Probability

- Ann. Probab.
- Volume 7, Number 1 (1979), 75-84.

### Some Stability Results for Vector Values Random Variables

#### Abstract

This paper explores the strong law of large numbers in the infinite dimensional setting. It is shown that under several classical conditions--such as the Kolmogorov condition--the strong law holds if and only if the weak law holds.

#### Article information

**Source**

Ann. Probab., Volume 7, Number 1 (1979), 75-84.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176995149

**Digital Object Identifier**

doi:10.1214/aop/1176995149

**Mathematical Reviews number (MathSciNet)**

MR515814

**Zentralblatt MATH identifier**

0399.60007

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B05: Probability measures on topological spaces

Secondary: 60F15: Strong theorems 60F05: Central limit and other weak theorems 60F10: Large deviations

**Keywords**

Strong law of large numbers weak law of large numbers Erdos double truncation exponential inequalities

#### Citation

Kuelbs, J.; Zinn, Joel. Some Stability Results for Vector Values Random Variables. Ann. Probab. 7 (1979), no. 1, 75--84. doi:10.1214/aop/1176995149. https://projecteuclid.org/euclid.aop/1176995149