The Topology of Information on the Space of Probability Measures over\n Polish Spaces

2013/07/15 by Abhishek Gupta, Gupta, Abhishek
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Economic theories and models #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1307.3989

openalex publication_date 2013/07/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study here the topology of information on the space of probability\nmeasures over Polish spaces that was defined in [1]. We show that under this\ntopology, a convergent sequence of probability measures satisfying a\nconditional independence property converges to a measure that also satisfies\nthe same conditional independence property. In the process of showing this, we\nalso provide a correct proof of the result in Lemma 4 in [1].\n

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