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June, 1962 Relations between Weak and Uniform Convergence of Measures with Applications
R. Ranga Rao
Ann. Math. Statist. 33(2): 659-680 (June, 1962). DOI: 10.1214/aoms/1177704588


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.


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R. Ranga Rao. "Relations between Weak and Uniform Convergence of Measures with Applications." Ann. Math. Statist. 33 (2) 659 - 680, June, 1962.


Published: June, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0117.28602
MathSciNet: MR137809
Digital Object Identifier: 10.1214/aoms/1177704588

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 2 • June, 1962
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