A new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of Banach space valued random elements

Cabrera M. O., Rosalsky A., ÜNVER M., Volodin A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.487, no.1, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 487 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1016/j.jmaa.2020.123975
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Real separable Banach space, Array of random elements, Weighted sums, Compact uniform integrability, Mean convergence, LARGE NUMBERS, LAWS
  • Ankara University Affiliated: Yes

Abstract

In this correspondence, for an array {Xnk : un < k < E N} of integrable random elements in a real separable Banach space and an array {a,, : u < k < n E N} of real numbers, a new type of compact uniform integrability is introduced and it is used to obtain degenerate mean convergence theorems for the weighted V, sums E a k(X.,,,k n E N. More specifically, conditions are provided k=u under which lim E n-400 E a,,k(Xnk EX k) k=u, = 0. 2020 Elsevier Inc. All rights reserved.