A note on the de La Vallée Poussin criterion for uniform integrability

DOI10.1016/j.spl.2010.10.015zbMath1205.60008OpenAlexW2052886600MaRDI QIDQ618029

Andrew Rosalsky, Tien-Chung Hu

Publication date: 14 January 2011

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2010.10.015

zbMATH Keywords

convergence of integralstightness of distribution functionsweak convergence of distribution functions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probabilistic measure theory (60A10)

Related Items (8)

On uniform nonintegrability for a sequence of random variables ⋮ On the concept of \(B\)-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense ⋮ A note on the Malliavin-Sobolev spaces ⋮ De la Vallée Poussin's theorem, uniform integrability, tightness and moments ⋮ Uniform nonintegrability of random variables ⋮ A note on stochastic dominance, uniform integrability and lattice properties ⋮ A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers ⋮ Some results concerning ideal and classical uniform integrability and mean convergence

Cites Work

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• \(\mathfrak G\)-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space
• A note on the rate of convergence of a mean
• DE LA VALLÉE POUSSIN'S THEOREM AND WEAKLY COMPACT SETS IN ORLICZ SPACES
• The de la Vallée Poussin theorem for vector valued measure spaces
• Modes of convergence: Interpolation methods. I

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