2014/02/25 by Barbie, Martin, Gupta, Abhishek
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)
paper · doi:10.48550/arxiv.1402.6364
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.