The portmanteau theorem for Dedekind complete Riesz space-valued measures. (English) Zbl 1076.28004

Takahashi, Wataru (ed.) et al., Nonlinear analysis and convex analysis. Proceedings of the 3rd international conference
(NACA2003), Tokyo, Japan, August 25–29, 2003. Yokohama: Yokohama Publishers (ISBN 4-946552-15-4/hbk). 149-158 (2004).
The Portmanteau theorem gives several equivalent conditions for weak convergence of a net of positive real-valued Borel measures. The author generalizes this theorem for measures with values in Dedekind complete Riesz spaces.
For the entire collection see [Zbl 1063.00012].
Reviewer: Hans Weber (Udine)


28A33 Spaces of measures, convergence of measures
28B15 Set functions, measures and integrals with values in ordered spaces
46G10 Vector-valued measures and integration