On the Concept of <i>A</i>-Statistical Uniform Integrability and the Law of Large Numbers

Giuliano Antonini R., Unver M., Volodin A.

LOBACHEVSKII JOURNAL OF MATHEMATICS, vol.40, no.12, pp.2034-2042, 2019 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 12
  • Publication Date: 2019
  • Doi Number: 10.1134/s1995080219120035
  • Journal Name: LOBACHEVSKII JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.2034-2042
  • Keywords: Sequence of random variables, uniform integrability, statistical convergence, APPROXIMATION THEOREMS, RANDOM-VARIABLES, WEIGHTED SUMS, CONVERGENCE, SUMMABILITY, OPERATORS, SPACES
  • Ankara University Affiliated: Yes

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.