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On the Concept of A-Statistical Uniform Integrability and the Law of Large Numbers

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Abstract

In this paper, we introduce the concept of A-statistical uniform integrability of sequences of random variables which is not only more general than the concept of uniform integrability, but is also weaker than the concept of uniform integrability. We also give some characterizations of A-statistical uniform integrability and prove a law of large numbers.

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Funding

The research of M. Ünver was done while he was visiting University of Regina, Canada and the research has been supported by The Scientific and Technological Research Council of Turkey (TÜBITAK) Grant 1059B191800534. A part of research of A. Volodin has been done during the visit to the University of Pisa in December 2016. The authors would like to express their appreciation to the INDAM for supporting this visit.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    R. Giuliano Antonini

  2. Department of Mathematics, Faculty of Science, Ankara University, Beşevler, 06100, Ankara, Turkey

    M. Ünver

  3. Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada, S4S 0A2

    A. Volodin

Authors
  1. R. Giuliano Antonini
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  2. M. Ünver
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  3. A. Volodin
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Corresponding authors

Correspondence to R. Giuliano Antonini, M. Ünver or A. Volodin.

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Submitted by A.M. Elizarov

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Giuliano Antonini, R., Ünver, M. & Volodin, A. On the Concept of A-Statistical Uniform Integrability and the Law of Large Numbers. Lobachevskii J Math 40, 2034–2042 (2019). https://doi.org/10.1134/S1995080219120035

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  • DOI: https://doi.org/10.1134/S1995080219120035

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