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

2015/09/10 by Seyed-Mohammad Bagheri, Seyed‐Mohammad Bagheri, Bagheri, Seyed-Mohammad +2
Computer Science · Mathematics · #03B48 #03C20 #03C45 #46B50 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03B48 #msc:03C20 #msc:03C45 #msc:46B50

paper · pdf · doi:10.48550/arxiv.1509.03193

This paper has been withdrawn by the author due to a crucial sign error

openalex publication_date 2015/09/10 · arxiv created 2015/09/20 · arxiv updated 2015/09/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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