Proofs for Folklore Theorems on the Radon-Nikodym Derivative
Yaiza Bermudez, Gaetan Bisson, Iñaki Esnaola, Samir M. Perlaza
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.