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
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.
Ann. Math. Statist., Volume 33, Number 2 (1962), 659-680.
First available in Project Euclid: 27 April 2007
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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