Integration in Riesz spaces with respect to \((D)\)-convergence. (English) Zbl 0918.28010

Boccuto, Antonio

Tatra Mt. Math. Publ. 10, 33-54 (1997).

Let \(R_1\) and \(R_2\) be Riesz spaces. In the paper there are introduced some integrals of \(R_1\)-valued mappings with respect to finitely additive \(R_2\)-valued means. There are proved Vitali-type convergence theorems and Scheffé-type theorems with respect to \((D)\)-convergence.

Reviewer: Miloslav Duchoň (Bratislava)

MSC:

28B05	Vector-valued set functions, measures and integrals
46G10	Vector-valued measures and integration

Keywords:

Riesz space; convergence theorems; integration