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A Compact Topology for Sigma-Algebra Convergence

Author

Listed:
  • Beissner, Patrick

    (HU Berlin)

  • Tölle, Jonas

    (Uni Augsburg)

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.

Suggested Citation

  • Beissner, Patrick & Tölle, Jonas, 2018. "A Compact Topology for Sigma-Algebra Convergence," Rationality and Competition Discussion Paper Series 74, CRC TRR 190 Rationality and Competition.
    • Handle: RePEc:rco:dpaper:74
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    References listed on IDEAS

    as
    1. Khan, M. Ali & Sun, Yeneng & Tourky, Rabee & Zhang, Zhixiang, 2008. "Similarity of differential information with subjective prior beliefs," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 1024-1039, September.
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    3. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
    4. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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