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

Giuliano Antonini, R.; Unver, MEHMET; Volodin, A.

doi:10.1134/s1995080219120035

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)

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.