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

Abstract

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].