Research Article

Generating functions in Riesz spaces

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 , 2024 , pages: 1–21

DOI: 10.2989/16073606.2023.2287853

Author(s): Youssef Azouzi Tunis-El Manar University, Tunisia , Youssef Nasri Tunis-El Manar University, Tunisia

Keywords: 47B65 , 47B60 , 46C50 , 46E40 , 46A40 , 46A20 , 46B40 , Generating function , Dedekind complete Riesz space , Conditional expectation , order convergence , unbounded order convergence

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Abstract

We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectation operator. This allows us to study discrete processes in a free-measure setting. In particular we improve a result obtained by Kuo, Vardy and Watson concerning Poisson approximation.

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