Probability links: measure theory and sigma-algebras

Ina is taking a statistics course this fall, for which the prof recommended real analysis as a prerequisite. Turns out he's doing probability in quite a bit of detail. It must be b/c it's through the Econ dept.

So Ina asked me last night about the definition of a sigma-algebra. We were at Vesuvio at the time, so I told her I'd check my analysis texts at home. Royden has the material, but I figured it would be easier to send her some links. I e-mailed them to her, but figured I'd also post them here:

GooglePrint has a lot of material. Here is one titled Real Analysis and Probability that could be a good reference. But it seems like its aimed at readers already familiar with real analysis and probability. Probably a better option would be this: A First Look at Rigorous Probability Theory by J.S. Rosenthal.

It just occurred to me that I have Durrett's Probabilty: Theory and Examples at home as well. Another Cornell text that Amazon turned up, and which looks like it could be appropriate: A Probability Path by Sidney Resnick.

Amazon also led me to Billingsley's Probability and Measure, which I believe is a classic text, but again might be aimed for a more mathematically mature audience. It also led me to a couple more texts on stochastic processes (by Resnick and Durrett, actually) that I might need to take a look at sooner or later.

But to get started, the wikipedia entries for measure theory and sigma-algebra look pretty good.