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

Martin Barbie, Abhishek Gupta

Published 2014-02-25Version 1

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.