
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.
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