In this paper we give some examples and applications of sandwich, extension and Hahn-Babach-type theorems for vector lattice-valued functionals to asymptotic densities, ergodic-type theorems, and exchangeable processes. We find that, in these applications, one is led to study the continuity of the involved means, and we present some examples of both continuous and non-continuous invariant mappings. We give necessary and/or sufficient conditions for the existence of continuous invariant means, and for the continuity of all invariant means, taking values in a Dedekind complete Riesz space. Finally, one can ask if theorems of this kind remain true, if we take a general lattice group instead of a Riesz space: we prove that the answer is substantially "negative".
Continuous invariant vector-valued means and applications
BOCCUTO, Antonio
1995
Abstract
In this paper we give some examples and applications of sandwich, extension and Hahn-Babach-type theorems for vector lattice-valued functionals to asymptotic densities, ergodic-type theorems, and exchangeable processes. We find that, in these applications, one is led to study the continuity of the involved means, and we present some examples of both continuous and non-continuous invariant mappings. We give necessary and/or sufficient conditions for the existence of continuous invariant means, and for the continuity of all invariant means, taking values in a Dedekind complete Riesz space. Finally, one can ask if theorems of this kind remain true, if we take a general lattice group instead of a Riesz space: we prove that the answer is substantially "negative".I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
