A compact topology for sigma-algebra convergence
- 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.
| Author: | Patrick Beissner, Jonas M. TölleGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/73448 |
| URL: | https://rationality-and-competition.de/2018/02/21/a-compact-topology-for-sigma-algebra-convergence/ |
| Publisher: | Collaborative Research Center Transregio 190 |
| Type: | Working Paper |
| Language: | English |
| Year of first Publication: | 2018 |
| Release Date: | 2020/03/28 |
| Pagenumber: | 24 |
| Series: | Collaborative Research Center Transregio 190, Discussion Paper ; 74 |
| DOI: | https://doi.org/10.5282/ubm/epub.58084 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis |
