Resolution of the Borel-Kolmogorov Paradox via the Maximum Entropy Principle

Abstract: 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.