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.
Original language | English |
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Article number | 3 |
Pages (from-to) | 33-47 |
Number of pages | 14 |
Journal | Theoretical Mathematics & Applications |
Volume | 6 |
Issue number | 3 |
Publication status | Published - Aug 2016 |
Keywords
- Riesz spaces
- Ultrafilter Theorem
- Compactness