This paper presents a rigorous resolution of the Borel-Kolmogorov paradox using the Maximum Entropy Principle. We construct a metric-based framework for Bayesian inference that uniquely extends conditional probability to events of null measure. The results unify classical Bayes' rules and provide a robust foundation for Bayesian inference in metric spaces.

翻译：本文利用最大熵原理，对波莱尔-柯尔莫哥洛夫悖论提出了严格的解析方案。我们构建了一个基于度量的贝叶斯推断框架，该框架能够将条件概率唯一地扩展到零测度事件上。研究结果统一了经典贝叶斯规则，并为度量空间中的贝叶斯推断奠定了坚实的理论基础。