On Multiple and Polynomial Recurrent extensions of infinite measure preserving transformations

TL;DR

This paper proves that certain recurrence properties in infinite measure preserving transformations are preserved under extensions, advancing understanding of their structural behavior.

Contribution

It introduces the result that multiple and polynomial recurrence properties are inherited by extensions of infinite measure preserving transformations.

Findings

Recurrence properties pass to extensions

Extension of transformations preserves multiple recurrence

Extension of transformations preserves polynomial recurrence

Abstract

We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.