Locally standard measure algebras

TL;DR

This paper introduces a parameterization of countable locally standard measure algebras using pairs of a Steinitz number and a real number ≥ 1, extending classical theorems in the field.

Contribution

It provides a new classification framework for measure algebras, generalizing previous results by Dixmier and Baranov.

Findings

Countable locally standard measure algebras are parameterized by Steinitz numbers and real numbers ≥ 1.

The classification extends classical theorems to a broader class of measure algebras.

The approach offers a new perspective on the structure of measure algebras.

Abstract

We parameterize countable locally standard measure algebras by pairs of a Steinitz number and a real number greater or equal to 1. This is an analog of the theorems of J.Dixmier and A.A.Baranov.