The Annals of Mathematical Statistics

Relations between Weak and Uniform Convergence of Measures with Applications

R. Ranga Rao

Full-text: Open access

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: 27 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177704588

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177704588

Mathematical Reviews number (MathSciNet)
MR137809

Zentralblatt MATH identifier
0117.28602

Citation

Rao, R. Ranga. Relations between Weak and Uniform Convergence of Measures with Applications. The Annals of Mathematical Statistics 33 (1962), no. 2, 659--680. doi:10.1214/aoms/1177704588. http://projecteuclid.org/euclid.aoms/1177704588.


Export citation