We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which provide an abstract categorical framework for probability and information flow. The diagrammatic and abstract nature of the arguments makes the proof intuitive and easy to follow. We also show how the usual measure-theoretic version of de Finetti's Theorem for standard Borel spaces is an instance of this result.

翻译：我们提出了一个新颖的证明,证明德法林蒂理论的理论,该理论以无限变量序列的变异-变异概率尺度为特征,即所谓的可交换措施。该证据用马尔科夫类别的语言表述,为概率和信息流动提供了抽象的绝对框架。这些论点的图表和抽象性质使证据直观和容易遵循。我们还展示了标准波雷尔空间的德法林蒂理论的通常测量-理论版本是如何体现这一结果的。