Theoretical Mathematics & Applications

Invariant Means on σ-Dedekind complete totally ordered Riesz Spaces

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• Abstract

  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.