The Topology of Information on the Space of Probability Measures over Product of Polish Spaces
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 measures spaces under which a convergent sequence of probability measures is also convergent in the topology of information.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 DOI:
 10.48550/arXiv.1402.6364
 arXiv:
 arXiv:1402.6364
 Bibcode:
 2014arXiv1402.6364B
 Keywords:

 Mathematics  Probability;
 Mathematics  Optimization and Control
 EPrint:
 30 pages, submitted to Journal of Mathematical Economics