A note on Riesz space valued measures

TAN N. Ö.

Turkish Journal of Mathematics, vol.40, no.1, pp.114-121, 2016 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.3906/mat-1411-23
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.114-121
  • Keywords: Charge, Finitely additive measure, Outer measure, Riesz space valued measure
  • Uşak University Affiliated: Yes

Abstract

In this paper, some properties of Riesz space valued measures that are defined on an algebra of sets are obtained. The question of under what conditions oba(F;E) = α(F;E) for a given Dedekind complete Riesz space E is answered under natural conditions. The outer measure, which is generated by order bounded Riesz space valued measure, is obtained and its properties are investigated. The concept of hazy convergence that is valid for real valued signed measures is extended to Riesz space valued measures. The consequences of order convergence of f:X → E, which implies hazy convergence, are given.