A Compact Topology for Sigma-Algebra Convergence

Beissner, Patrick; Tölle, Jonas (2018): A Compact Topology for Sigma-Algebra Convergence. Collaborative Research Center Transregio 190, Discussion Paper No. 74

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.

• Item Type: Paper (Discussion Paper)
• Keywords: convergence of sigma-algebras; compactness of sub-sigma-algebras; conditional expectation; fiber bundle; information economics.
• Faculties: Economics > Collaborative Research Center Transregio "Rationality and Competition"
• Subjects: 300 Social sciences > 330 Economics
• Language: English