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Uniformity for weak order convergence of Riesz space-valued measures

Published online by Cambridge University Press:  17 April 2009

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

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 265 - 274
Copyright
Copyright © Australian Mathematical Society 2005

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