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：我们遵循Baez与Fritz的理论精神，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。我们定义了一个适用于标准Borel空间上统计推断推理的范畴。我们将相对熵定义为映射至Lawvere范畴的函子，并论证了其凸性、下半连续性以及唯一性。