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Dieudonné-type theorems for set functions with values in \((l)\)-groups. (English) Zbl 1067.28011

A theorem of Dieudonné essentially says that an equibounded sequence of regular \(\sigma\)-additive real-valued measures converging on all open sets converges on all Borel sets and that the limit function is a regular \(\sigma\)-additive measure. The authors generalize this theorem for \(l\)-group-valued measures. A crucial point is here the use of a suitable convergence in \(l\)-groups. Moreover, the authors replace the system of open and the system of closed sets by abstract lattices.
Reviewer: Hans Weber (Udine)

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
28B10 Group- or semigroup-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
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