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：我们对与措施保全功能有关的香农信息损失的Baez-Fritz-Leinster定性提供了一种随机延伸,这收回了有条件的酶和我们称之为“有条件信息损失”的密切相关的信息理论计量。 虽然不是补充,但这些信息计量是半全局性的,我们在任何马尔科夫类别中都引入了这种概念。我们还为信息计量引入了“非热带海湾”规则的概念,我们从这一规则的角度对有条件的酶进行了定性。