A Note on Uniform Nonintegrability of Random Variables

Ze-Chun Hu; Xue Peng

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arXiv · 1605.05434

A Note on Uniform Nonintegrability of Random Variables

Ze-Chun Hu·Xue Peng

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Abstract

In a recent paper \cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in \cite{CHR16}.

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Ze-Chun Hu, Xue Peng. 2016-06-07. A Note on Uniform Nonintegrability of Random Variables. https://arxiv.org/abs/1605.05434

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