New versions of the Daniell-Stone-Riesz representation theorem

Heinz König ()
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Heinz König: Universität des Saarlandes, Fakultät für Mathematik und Informatik

A chapter in Measure and Integration, 2012, pp 405-418 from Springer

Abstract: Abstract The traditional representation theorems after Daniell-Stone and Riesz were in a kind of separate existence until Pollard-Topsøe 1975 and Topsøe 1976 were the first to put them under common roofs. In the same spirit the present article wants to obtain a unified representation theorem in the context of the author’s work in measure and integration. It is an inner theorem like the previous ones. The basis is the recent comprehensive inner Daniell-Stone theorem, so that in particular there are no a priori assumptions on the additive behaviour of the data.

Keywords: Daniell-Stone and Riesz representation theorems; Stonean lattices and Stonean lattice cones; Inner premeasures; Inner extensions; Inner envelopes; Choquet integral; Set-theoretical compactness (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0382-3_19

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DOI: 10.1007/978-3-0348-0382-3_19

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