A constructive proof of the Bollob\'as-Varopoulos theorem

TL;DR

This paper provides a constructive proof of a finite version of the Bollobás-Varopoulos theorem, an analogue of Hall's matching theorem for non-atomic measure spaces, enhancing understanding with explicit construction methods.

Contribution

It introduces a fully constructive proof for the finite case of the Bollobás-Varopoulos theorem, previously known through non-constructive methods.

Findings

Established a constructive proof for the finite version of the theorem

Enhanced the understanding of measure space matchings with explicit methods

Provided a foundation for algorithmic applications in measure theory

Abstract

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.