On the exactness of the Levy-transformation

TL;DR

This paper demonstrates that a sufficient condition for the strong mixing property of the Levy-transformation actually implies the much stronger property of exactness, refining previous understanding.

Contribution

It proves that the condition ensuring strong mixing for the Levy-transformation also guarantees its exactness, a stronger ergodic property.

Findings

The Levy-transformation is exact under the given condition.

Exactness implies stronger ergodic properties than strong mixing.

The result refines previous conditions for the Levy-transformation.

Abstract

In a recent paper we gave a sufficient condition for the strong mixing property of the Levy-transformation. In this note we show that it actually implies a much stronger property, namely exactness.