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Chandra, Hu and Rosalsky  [1]   introduced the notion of a sequence of random variables being uniformly nonintegrable and they established a de La Vallée Poussin type criterion for this notion. Inspired by the Chandra, Hu and Rosalsky  [1]   article, Hu and Peng  [2]   introduced the weaker notion of a sequence of random variables being weakly uniformly nonintegrable and they also established a de La Vallée Poussin type criterion for this notion using a modification of the Chandra, Hu and Rosalsky  [1]   argument. In this correspondence, we introduce the more general notion of uniform nonintegrability and weak uniform nonintegrability with respect to an array of nonnegative real numbers together with a de La Vallée Poussin type criterion for this notion. This criterion immediately yields as particular cases the criteria of Chandra, Hu and Rosalsky  [1]   and Hu and Peng  [2]  , and it has a substantially simpler and more straightforward proof.

On Uniform Nonintegrability and Weak Uniform Nonintegrability of a Sequence of Random Variables with Respect to a Nonnegative Array