### 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

## Fingerprint Dive into the research topics of 'Invariant Means on Dedekind complete totally ordered Riesz Spaces'. Together they form a unique fingerprint.

## Cite this

Chailos, G., & Aristidou, M. (2016). Invariant Means on Dedekind complete totally ordered Riesz Spaces.

*Theoretical Mathematics & Applications*,*6*(3), 33-47. [3].