I am currently working in communications, where a lot of work is done via probability calculations (densities and such). As I am not a mathematician, I do have a quite hard time understanding one specific aspect. I know what the mathematical definition looks like, but I just can't really find a way to imagine it in terms of things I know about stocastics and probability theory.
So here is my problem: In the work of a specific author, he doesn't deal with densities, but with Radon-Nikodym derivates instead.
One example would be the Kullback-Leibler-divergence. I "know" it as $D(P||Q) = \int p(x) log \frac{p(x)}{q(x)} dx$ where p and q are some pdfs.
Whereas in his work he states it as $D(P||Q) = \int \frac{dP}{dQ} log \frac{dP}{dQ} \cdot dQ$ (I know that this formula can also be found on wikipedia) with $ \frac{dP}{dQ} $ being the Radon-Nikodym derivative
So here is the actual question: How or what can I imagine this Radon-Nikodym derivative to be like? Comparing the formulas, in this case it would be something like "dP = p(x)".
I am thankful for any explanation or reading tips, but please don't just answer the definition. I looked it up. I want to really understand what it means.