Generating Product Systems

TL;DR

This paper extends Krieger's finite generation theorem by establishing conditions under which an ergodic system can be generated by two partitions with specific measurability and size constraints.

Contribution

It introduces new criteria for generating ergodic systems using pairs of partitions with prescribed properties, generalizing previous finite generation results.

Findings

Conditions for generating ergodic systems with two partitions

Partitions measurable with respect to a sub-algebra

Partitions of fixed size

Abstract

Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.