We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we call conditional information loss. Although not functorial, these information measures are semi-functorial, a concept we introduce that is definable in any Markov category. We also introduce the notion of an entropic Bayes' rule for information measures, and we provide a characterization of conditional entropy in terms of this rule.

翻译：我们为香农信息损失的Baez-Fritz-Leinster定性提供了与措施保存功能有关的“Baez-Fritz-Leinster”特征的延伸。这收回了有条件的酶和我们称之为“有条件的信息损失”的密切相关的信息理论测量。虽然不是“functor”的,但这些信息测量措施是半硬体的,这是我们在任何马尔科夫类别中都可定义的概念。我们还引入了对信息计量的“对热带海湾规则”的概念,我们根据这一规则对有条件的酶进行了定性。