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arXiv · 2509.24735

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

Raphaël Trésor·Mykola Lukashchuk
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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.

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Raphaël Trésor, Mykola Lukashchuk. 2025-09-29. Resolution of the Borel-Kolmogorov Paradox via the Maximum Entropy Principle. https://arxiv.org/abs/2509.24735

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