Life without "Choice"

TL;DR

This paper presents an AC-independent proof of a non-measurable set's existence, deriving from the Hahn-Banach theorem, which is weaker than the Axiom of Choice.

Contribution

It provides a novel proof of a non-measurable set that does not rely on the Axiom of Choice, unlike traditional proofs.

Findings

Existence of a non-measurable set proven without AC

Uses Hahn-Banach theorem as core tool

Demonstrates weaker assumptions suffice for such existence

Abstract

We propose an AC-independent proof of the existence of a non-measurable set as a consequence of the Hahn-Banach theorem of functional analysis which is known to be strictly weaker than AC.