Invariant Means on Dedekind complete totally ordered Riesz Spaces

George Chailos, Michael Aristidou

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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.
Original languageEnglish
Article number3
Pages (from-to)33-47
Number of pages14
JournalTheoretical Mathematics & Applications
Issue number3
Publication statusPublished - Aug 2016


  • Riesz spaces
  • Ultrafilter Theorem
  • Compactness

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