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.

中文翻译：

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关于条件独立和无条件独立之间的关系及其对马尔可夫核的扩展的注解

作为本文主要结果的结果，获得了关于条件独立性和无条件独立性之间关系的两个已知结果，一个定理使用马尔可夫核的独立性来获得添加到条件独立性意味着独立性的最小条件。给出了一些反例和表示结果，以阐明所引入的概念和主定理陈述的命题。此外，条件独立性和上述结果被扩展到马尔可夫核的框架。