## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 33, Number 2 (1962), 659-680.

### Relations between Weak and Uniform Convergence of Measures with Applications

#### Abstract

In this paper the relation between weak convergence of a sequence of measures and uniform convergence over certain classes of continuity sets (or uniform convergence of the integrals over certain classes of continuous functions) is studied. These results are applied to obtain laws of large numbers for random functions and generalizations of the Glivenko-Cantelli lemma.

#### Article information

**Source**

Ann. Math. Statist. Volume 33, Number 2 (1962), 659-680.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177704588

**Digital Object Identifier**

doi:10.1214/aoms/1177704588

**Mathematical Reviews number (MathSciNet)**

MR137809

**Zentralblatt MATH identifier**

0117.28602

**JSTOR**

links.jstor.org

#### Citation

Rao, R. Ranga. Relations between Weak and Uniform Convergence of Measures with Applications. Ann. Math. Statist. 33 (1962), no. 2, 659--680. doi:10.1214/aoms/1177704588. https://projecteuclid.org/euclid.aoms/1177704588