(adsbygoogle = window.adsbygoogle || []).push({}); "Concrete" non-measurable sets

I've had Vitali's proof of the existence of non-(Lebesgue) measurable sets branded into the side of my brain over the years. However, the proof always critically relies on evoking the axiom of choice. Has anybody every demonstrated a non-AoC construction of a non-measurable set? Or do the intuitionist logicians just avoid measure theory all together?

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# Concrete non-measurable sets

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