Existence of Infinite Product Measures

TL;DR

This paper introduces a new method for constructing product measures for any sequence of measure spaces using outer measure techniques, broadening the scope of previous results.

Contribution

It generalizes existing product measure constructions by removing restrictions on the measure spaces involved.

Findings

Successfully constructs product measures without conditions on measure spaces

Extends the applicability of product measure theory

Provides a new framework for measure space analysis

Abstract

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.