Chennai Mathematical Institute


3:30 pm, Lecture Hall 802
A category of probability spaces and a conditional expectation functor

Yoshihiro Ryu
Ritsumeikan University, Japan.


We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving direction of information with a way of its interpretation. We introduce a contravariant functor E from Prob to Set, the category of sets. The functor E provides conditional expectations along arrows in Prob, which are generalizations of the classical conditional expectations. For a Prob-arrow f^{-}, we introduce two concepts f^{-}-measurability and f^{-}-independence and investigate their interaction with conditional expectations along f^{-}.