A Compact Topology for Sigma-Algebra Convergence

Patrick Beissner and Jonas Tölle
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Patrick Beissner: HU Berlin
Jonas Tölle: Uni Augsburg

No 74, Rationality and Competition Discussion Paper Series from CRC TRR 190 Rationality and Competition

Abstract: We propose a sequential topology on the collection of sub-sigma-algebras included in a separable probability space. We prove compactness of the conditional expectations with respect to L2-bounded random variables along sequences of sub-sigma-algebras. The varying index of measurability is captured by a bundle space construction. As a consequence, we establish the compactness of the space of sub-sigma-algebras. The proposed topology preserves independence and is compatible with join and meet operations. Finally, a new application to information economics is discussed.

Keywords: convergence of sigma-algebras; compactness of sub-sigma-algebras; conditional expectation; fiber bundle; information economics. (search for similar items in EconPapers)
Date: 2018-02-21
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