A type III_1 Bernoulli shift

TL;DR

This paper constructs a specific product measure making the shift on a two-point space a type III_1 transformation, advancing understanding of ergodic theory and measure-preserving systems.

Contribution

It introduces a novel construction of a product measure that results in a type III_1 shift, providing new examples in ergodic theory.

Findings

Demonstrates existence of a type III_1 shift under a specific measure

Advances the classification of ergodic transformations

Provides a new example in the theory of measure-preserving systems

Abstract

We provide a construction of a product measure under which the shift on the two point product space is a type III_1 transformation.