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.

翻译：本文遵循Baez与Fritz的思路，对定义在标准Borel空间上的概率分布的相对熵进行了范畴论处理。我们构造了一个适用于标准Borel空间上统计推理的范畴。将相对熵定义为一个取值于Lawvere范畴的函子，并证明了其凸性、下半连续性与唯一性。