We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By means of this method, we prove versions of Varadhan and Bryc theorems, and a conditional version of Cramér theorem.

中文翻译：

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随机集和马尔可夫核的布尔值表示及其在大偏差中的应用

通过显示布尔值模型中的Borel集，Borel函数和Borel概率度量分别表示随机Borel集，随机Borel函数和Markov核，我们在随机集理论和布尔值分析之间建立了联系。这使得布尔值传递原理能够获得可用定理的随机集合类似物。作为一种应用，我们为大偏差理论建立了布尔值传递原理，该原理允许系统地解释大偏差理论作为马尔可夫核的版本的结果。通过这种方法，我们证明了Varadhan和Bryc定理的形式，以及Cramér定理的条件形式。