4 papers
Uniform Integrability in vector lattices and applications
Youssef Azouzi
In this paper, we explore an abstraction of uniform integrability in vector lattices and demonstrate its application by providing a positive solution to an open question posed by K…
A diagonal principle for nets
Youssef Azouzi
In our work, we provide a constructive proof of a generalized version of Cantor's diagonal argument for nets. This result expands the well-known technique beyond sequences, allowin…
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…