标题： 关于条件独立与无条件独立关系的注记及其对马尔可夫核的扩展 显示英文标题

标题： A Note on the Relationship Between Conditional and Unconditional Independence, and its Extensions for Markov Kernels

摘要： 本文的主要定理——利用马尔可夫核的独立性来得到使条件独立蕴含独立的最小条件——得出两个关于条件独立与无条件独立之间关系的已知结果作为推论。此外，还提供了一些反例和表示结果，以阐明引入的概念和主要定理命题中的命题。 此外，还将条件独立性和上述结果推广到了马尔可夫核框架下。 显示英文摘要

摘要： Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which added to conditional independence implies independence. Some counterexamples and representation results are provided to clarify the concepts introduced and the propositions of the statement of the main theorem. Moreover, conditional independence and the mentioned results are extended to the framework of Markov kernels.