On uniform nonintegrability for a sequence of random variables

In this correspondence, we introduce the notion of a sequence of random variables being uniformly nonintegrable. Sufficient and, separately, necessary conditions for uniform nonintegrability are presented and we also establish two equivalent characterizations of uniform nonintegrability, one of which is a uniform nonintegrability analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. Several illustrative examples are presented.