4 papers
A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices
Youssef Azouzi, Marwa Masmoudi, Bruce Alastair Watson
Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the me…
Some characterizations of ergodicity in Riesz spaces
Youssef Azouzi, Marwa Masmoudi
In the recent surge of papers on ergodic theory within Riesz spaces, this article contributes by introducing enhanced characterizations of ergodicity. Our work extends and strength…
Conditional supremum in Riesz spaces and applications
Youssef Azouzi, Mohamed Amine Ben Amor, Dorsaf Cherif +1
We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool…
The Kac formula and Poincaré recurrence theorem in Riesz spaces
Youssef Azouzi, Mohamed Amine Ben Amor, Jonathan Homann +2
Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional v…