### Abstract

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 |

### Fingerprint

### Keywords

- Riesz spaces
- Ultrafilter Theorem
- Compactness

### Cite this

*Theoretical Mathematics & Applications*,

*6*(3), 33-47. [3].

}

*Theoretical Mathematics & Applications*, vol. 6, no. 3, 3, pp. 33-47.

**Invariant Means on Dedekind complete totally ordered Riesz Spaces.** / Chailos, George; Aristidou, Michael.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Invariant Means on Dedekind complete totally ordered Riesz Spaces

AU - Chailos, George

AU - Aristidou, Michael

PY - 2016/8

Y1 - 2016/8

N2 - 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.

AB - 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.

KW - Riesz spaces

KW - Ultrafilter Theorem

KW - Compactness

M3 - Article

VL - 6

SP - 33

EP - 47

JO - Theoretical Mathematics & Applications

JF - Theoretical Mathematics & Applications

SN - 1792-9687

IS - 3

M1 - 3

ER -