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Autoren: 
Beissner, Patrick
Tölle, Jonas
Datum: 
2018
Schriftenreihe/Nr.: 
Discussion Paper No. 74
Zusammenfassung: 
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.
Schlagwörter: 
convergence of sigma-algebras
compactness of sub-sigma-algebras
conditional expectation
fiber bundle
information economics
Dokumentart: 
Working Paper

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