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Uniform integrability and local convexity in L0

Kardaras, Constantinos ORCID: 0000-0001-6903-4506 (2014) Uniform integrability and local convexity in L0. Journal of Functional Analysis, 266 (4). pp. 1913-1927. ISSN 0022-1236

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Identification Number: 10.1016/j.jfa.2013.12.008

Abstract

Let L0 be the vector space of all (equivalence classes of) real-valued random variables built over a probability space (Ω,F,P), equipped with a metric topology compatible with convergence in probability. In this work, we provide a necessary and sufficient structural condition that a set X⊆L0 should satisfy in order to infer the existence of a probability Q that is equivalent to P and such that X is uniformly Q-integrable. Furthermore, we connect the previous essentially measure-free version of uniform integrability with local convexity of the L0-topology when restricted on convex, solid and bounded subsets of L0.

Item Type: Article
Official URL: http://www.journals.elsevier.com/journal-of-functi...
Additional Information: © 2014 Elsevier Inc
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Date Deposited: 14 Jan 2014 14:07
Last Modified: 20 Sep 2021 02:53
URI: http://eprints.lse.ac.uk/id/eprint/55273

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