A note on Riesz space valued measures

TAN N. Ö.

Turkish Journal of Mathematics, cilt.40, sa.1, ss.114-121, 2016 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3906/mat-1411-23
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.114-121
  • Anahtar Kelimeler: Charge, Finitely additive measure, Outer measure, Riesz space valued measure
  • Uşak Üniversitesi Adresli: Evet

Özet

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.