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arXiv:1307.3989 [math.PR]AbstractReferencesReviewsResources

The Topology of Information on the Space of Probability Measures over Polish Spaces

Abhishek Gupta

Published 2013-07-15, updated 2014-02-22Version 3

We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. 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. In the process of showing this, we also provide a correct proof of the result in Lemma 4 in [1].

Comments: Some proofs have been modified/elaborated and the paper has been expanded. Please see the new paper for correct proofs and more results on this topology
Categories: math.PR, math.FA, math.OC
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