# Proofs for Folklore Theorems on the Radon-Nikodym Derivative

arXiv: https://arxiv.org/abs/2501.18374 · HTML: https://mlsanity.com/paper/2501.18374/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 30 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [Optimal Bounds between f-Divergences and Integral Probability Metrics](https://mlsanity.com/paper/2006.05973/) (2020)
- [Empirical Risk Minimization with Relative Entropy Regularization](https://mlsanity.com/paper/2211.06617/) (2022)
- [An Information-Theoretic Approach to Generalization Theory](https://mlsanity.com/paper/2408.13275/) (2024)
- [f-divergences and their applications in lossy compression and bounding generalization error](https://mlsanity.com/paper/2206.11042/) (2022)
- [Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences](https://mlsanity.com/paper/2402.00501/) (2024)
- [Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2410.02833/) (2024)
- [The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms](https://mlsanity.com/paper/2411.12030/) (2024)

## Built on by (most cited first, 4 of 4)

- [Variations on the Expectation due to Changes in the Probability Measure](https://mlsanity.com/paper/2502.02887/) (2025)
- [Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms](https://mlsanity.com/paper/2604.20492/) (2026)
- [Empirical Risk Minimization with f-Divergence Regularization](https://mlsanity.com/paper/2601.13191/) (2026)
- [Machine Unlearning for Gibbs Supervised Learning Algorithms](https://mlsanity.com/paper/2609.29409/) (2026)

## Abstract (arXiv)

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.