Compactly uniform Bochner integrability of random elements


Unver M., Ulucay H.

POSITIVITY, vol.21, no.4, pp.1261-1272, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1007/s11117-017-0465-1
  • Journal Name: POSITIVITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1261-1272
  • Istanbul Technical University Affiliated: No

Abstract

As the concept of uniform integrability has an essential role in the convergence of moments and martingales in the probability theory it is important to study this concept. In the present paper using Bochner integral we define a new type of uniform integrability for sequences of random elements. We give some independent necessary and sufficient conditions for this concept. We also generalize the concepts of strong and statistical convergences to sequences of random elements and we obtain the relationship between these two important concepts of summability theory via this new type of uniform integrability.