Proofs for Folklore Theorems on the Radon-Nikodym Derivative
Yaiza Bermudez, Gaetan Bisson, I\~naki Esnaola, Samir M. Perlaza
TL;DR
This paper provides rigorous proofs for folklore theorems related to the Radon-Nikodym derivative, exploring their implications for probability measures and information theory.
Contribution
It offers formal proofs for folklore theorems and introduces a new interpretation of the sum of mutual and lautum information.
Findings
Formal proofs for folklore theorems on Radon-Nikodym derivatives
Identity involving mutual and lautum information
New interpretation of information sum
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.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · advanced mathematical theories · Topological and Geometric Data Analysis