A Note on Uniform Nonintegrability of Random Variables
Abstract
In a recent paper 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 Vall\'ee Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in CHR16.
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