An Information Theoretic Proof of the Radon-Nikodym Theorem

The Radon-Nikodym theorem plays a significant role in the definition of Shannon entropy, f-divergences, and other basic quantities in information theory. The existence of Radon Nikodym derivates appear in many text books in measure theory but in text books on probability or information theory it is often omitted because the proof is often considered to be too difficult.