Information theory from a (very pure) mathematician's perspective I'm a pure mathematician interested in learning about information theory. Unfortunately, I'm about as pure as they come - my specialty is mathematical logic, and I have absolutely no experience with programming or anything of a computational nature. I tried looking at Shannon's original paper, but the profusion of numbers intimidated me (I'm a mathematician after all!) When he starts discussing the particulars of coding specific alphabets, my brain begins to asking whether this attention to detail is really necessary and soon zones out... It took Church's thesis for granted some time ago. (Pathetic, I know.)

I'm wondering if there's some introduction to information theory written with people like me in mind. Something which uses the language of measure theory and recursion theory, and works in the greatest generality. Perhaps an expert in the area has written some notes in this direction as an idle folly? 

I realize that this might not be the place to ask this question, and apologize if this is the case.
I think you are looking for the topic of "Algorithmic Information Theory" (AIT). 
This area is the collision of information theory and computer science. For example "Information and Randomness: An Algorithmic Perspective" written by cristian calude contains interesting subjects in this area. You can find more in the AIT website.