Invariant Means on ?-Dedekind complete totally ordered Riesz Spaces

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Chailos, G.
Aristidou, Michael

Issue Date

2016

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Journal Article
Peer-Reviewed

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In this paper we consider the set B of all countable bounded subsets of V, where V is a totally ordered σ-Dedekind complete Riesz space equipped with the order topology. We show that on B there exists a function that in a sense behaves as an invariant " mean ". To do this, we construct a set of " approximately invariant means " and we show, using the Ultrafilter Theorem, that this set has a cluster point. This cluster point is the " invariant mean " on B that we are looking for. MSC: 47B37; 47B60; 54D30; 06B30

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