We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere's category and we show convexity, lower semicontinuity and uniqueness.

• 68-XX - Computer science
• 68Q85 - Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)