Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/185744
Authors: 
Beissner, Patrick
Tölle, Jonas
Year of Publication: 
2018
Series/Report no.: 
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.
Subjects: 
convergence of sigma-algebras
compactness of sub-sigma-algebras
conditional expectation
fiber bundle
information economics
Document Type: 
Working Paper

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