Bulletin of the Australian Mathematical Society

Research Article

Uniformity for weak order convergence of Riesz space-valued measures

Jun Kawabea1

a1 Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan, e-mail: jkawabe@shinshu-u.ac.jp

The purpose of the paper is to show that weak order convergence of a net of Dedekind complete Riesz space-valued σ-measures is uniform over uniformly bounded, uniformly equicontinuous classes of functions. The paper ends with generalizing Ulam's theorem for tightness of positive, finite Borel measures to Riesz space-valued σ-measures.

(Received October 26 2004)