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 |
|---|---|
| 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