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

2025/09/29 by Trésor, Raphaël, Lukashchuk, Mykola
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2509.24735

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.

Citations

• The lion in the attic -- A resolution of the Borel--Kolmogorov paradox

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