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The topology of information on the space of probability measures over Polish spaces

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  • Barbie, Martin
  • Gupta, Abhishek

Abstract

We study here the topology of information on the space of probability measures over Polish spaces that was defined in Hellwig (1996). We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence property converges to a measure that also satisfies the same conditional independence property. This also corrects the proof of a claim in Hellwig (1996, Lemma 4). Additionally, we determine sufficient conditions on the Polish spaces and the topology over measure spaces under which a convergent sequence of probability measures is also convergent in the topology of information.

Suggested Citation

  • Barbie, Martin & Gupta, Abhishek, 2014. "The topology of information on the space of probability measures over Polish spaces," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 98-111.
    • Handle: RePEc:eee:mateco:v:52:y:2014:i:c:p:98-111
    DOI: 10.1016/j.jmateco.2014.04.003
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