Eberlein-Smulian compactness and Kolmogorov extension theorems; a model theoretic approach

Abstract

This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was proved for bounded case in [8]. Second, we give a proof of the Eberlein-Smulian compactness theorem by Ramsey's theorem and point out the correspondence between this theorem and a result in Shelah's classification theory.

arXiv commentThis paper has been withdrawn by the author due to a crucial sign error