Right now I'm using the textbook "Real Analysis" by Royden. It is the book that concordia uses to teach both measure theory and real analysis. However, I am also supplementing my readings with course notes from various universities, online lectures and the internet in general. The internet is such an amazing place and it has become so easy to find lots of interesting things on it. Most of the measure theory I am learning however (the stuff not in the textbook) is related to eventually developing the notation of stochastic calculus. However, all the texts I'm using go through some quite rigorous presentations of what a measure space is and defining boreal sets, etc. So, they are still good texts.

Anyway, the coolest thing I've come arcoss so far in my measure theory learnings (or at least the coolest thing I can share over the internet without use of mathematical notation) is that the function f(x) = {1 is x is irrational and 0 if x is rational} is not a riemann integrable function. However, using measure theory and the lebesgue integral, we are able to evaluate this integral.

Anyway, the world of measure theory is much more fascinating than this, but it takes a while to explain some of its more profound results. I'm gonna try and get people to join the forum, but its would help if we could use Latex or some other form of math text input so that when we discuss problems, they are comprehensible.

Anyway, I guess I'll see you next week in complex analysis (there's a coop event this week so alas I will have to miss it).