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Representations of Archimedean Riesz spaces. - A survey. (English) Zbl 0922.46004

The goal of this paper is to give a survey of representation theorems in the theory of Archimedean Riesz spaces (or vector lattices).
The material is organized as follows: In Section 1, we collect important properties of Stonian spaces, since those spaces play an outstanding role in representation problems. Sections 2 and 3 are concerned with representations of “abstract” Riesz spaces, i.e., Riesz spaces which are not necessarily equipped with a compatible topology. In Section 4, we deal with Banach lattices, and finally, in Section 5, with Orlicz lattices.

MSC:

46A40 Ordered topological linear spaces, vector lattices
46B42 Banach lattices
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46B40 Ordered normed spaces
46E27 Spaces of measures
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
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References:

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