De la Vallée Poussin's theorem, uniform integrability, tightness and moments

DOI10.1016/j.spl.2015.08.011zbMath1356.60011OpenAlexW1186148100MaRDI QIDQ900936

Tapas Kumar Chandra

Publication date: 23 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.spl.2015.08.011

zbMATH Keywords

momentsuniform integrabilitytightnessCesàro uniform integrabilityuniform integrability in the Cabrera sense

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probabilistic measure theory (60A10) (L^p)-limit theorems (60F25)

Related Items (6)

On uniform nonintegrability for a sequence of random variables ⋮ 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 ⋮ The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure ⋮ Submodular mean field games: existence and approximation of solutions

Cites Work

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• Probability theory. A comprehensive course.
• Every random variable satisfies a certain nontrivial integrability condition
• On the Strong Law of Large Numbers and the Law of the Iterated Logarithm for Sequences of Independent Random Variables
• Measure and integration theory. Transl. from the German by Robert B. Burckel

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