Deep research in probability theory Recently I came across the concept of probability theory in my statistics class. I found the concept fascinating and plan to pursue it in depth.
Problem is, I'm an economics major and due to the the rigid education system in my country I can't pick up another subject along with it. I've decided to give it a go by myself. After searching for it I found out that measure theory and functional analysis is used for in depth research in probability. 
What I want to know is what topics do I have to cover before I get there and if you could name the books/sources you used, that would be much appreciated. If there's any autodidact out there do tell what sources you used as I understand this is on the very right side of the spectrum when it comes to difficulty.
 A: What you really need is Real Analysis, measure theory, and some comfort with elementary set theory.
I would recommend Rudin's book on Real and Complex Analysis.  He also wrote one on functional analysis as well (all when he was under something like 25).  They are sort of the standard texts many people use.  
I have never found a great text on the probability theory (the actual name of the theory of probability is often referred to as Mathematical Statistics).  I find that if you google it there are lots of professors who have written their own notes, essentially, you can download.  When I learned it the professor lectured it all from his head, as he said there weren't any good books.  
It is a a bit of a balancing act, trying to find something that you know enough math to make progress on the probability, then learning more math that underlies it, then back to probability, etc.
In fact, probability was not even on a firm mathematical footing until the Russian Mathematician Kolmogorov put it there well into the 1900s. 
