A Compact Topology for Sigma-Algebra Convergence


Beissner, Patrick (HU Berlin)
Tölle, Jonas (Uni Augsburg)


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.


convergence of sigma-algebras; compactness of sub-sigma-algebras; conditional expectation; fiber bundle; information economics.



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A Compact Topology for Sigma-Algebra Convergence