A non-product type non-singular transformation which satisfies Krieger's property A

TL;DR

This paper constructs an ergodic non-singular transformation that satisfies Krieger's property A but is not of product type, challenging previous assumptions about the relationship between these properties.

Contribution

It provides a counterexample demonstrating that satisfying Krieger's property A does not imply being of product type in non-singular transformations.

Findings

Existence of a non-product type transformation with property A

Counterexample to previous conjectures

Advances understanding of ergodic non-singular transformations

Abstract

We show that there exists an ergodic non-singular transformation which satisfies Krieger's property A, but which is not of product type.