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Uniform nonintegrability of random variables

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Abstract

Recently, T. K. Chandra, T. -C. Hu and A. Rosalsky [Statist. Probab. Lett., 2016, 116: 27–37] introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. We introduce a weaker definition on uniform nonintegrability (W-UNI) 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 by Chandra et al.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11371191).

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610064, China

    Zechun Hu & Xue Peng

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  1. Zechun Hu
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  2. Xue Peng
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Correspondence to Xue Peng.

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Hu, Z., Peng, X. Uniform nonintegrability of random variables. Front. Math. China 13, 41–53 (2018). https://doi.org/10.1007/s11464-017-0623-6

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  • DOI: https://doi.org/10.1007/s11464-017-0623-6

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