Proofs for Folklore Theorems on the Radon-Nikodym Derivative
Information Theory
2025-07-11 v3 History and Overview
math.IT
Statistics Theory
Machine Learning
Statistics Theory
Abstract
In this technical report, rigorous statements and formal proofs are presented for both foundational and advanced folklore theorems on the Radon-Nikodym derivative. The cases of conditional and marginal probability measures are carefully considered, which leads to an identity involving the sum of mutual and lautum information suggesting a new interpretation for such a sum.
Cite
@article{arxiv.2501.18374,
title = {Proofs for Folklore Theorems on the Radon-Nikodym Derivative},
author = {Yaiza Bermudez and Gaetan Bisson and Iñaki Esnaola and Samir M. Perlaza},
journal= {arXiv preprint arXiv:2501.18374},
year = {2025}
}
Comments
20 pages