Uniqueness of unbounded Loeb measure using Choquet’s theorem

Abstract

Uniqueness of the Carathéodory extension of the standard part map of an internal unbounded measure μ \mu defined on an internal algebra A \mathcal {A} of subsets of an internal set Ω \Omega has been proved by Henson using the notion of a countably determined set. Here we show how Choquet’s capacitability theorem can be used in the proof of the same result.