A note on Riesz space valued measures

Authors

NEŞET ÖZKAN TAN

DOI

10.3906/mat-1411-23

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 $oba(\mathcal{F},E)$ =$a(\mathcal{F},E)$ 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 $f:X\rightarrow E$, which implies hazy convergence, are given.

Keywords

Charge, finitely additive measure, outer measure, Riesz space valued measure

First Page

114

Last Page

121

Recommended Citation

TAN, NEŞET ÖZKAN (2016) "A note on Riesz space valued measures," Turkish Journal of Mathematics: Vol. 40: No. 1, Article 11. https://doi.org/10.3906/mat-1411-23
Available at: https://journals.tubitak.gov.tr/math/vol40/iss1/11