Question: I'm looking for good lecture notes (or concise books) that develop probability theory from a measure theoretic point of view. In particular, I'm looking for a text where the measure theoretic part is developed only as far as needed for probability theory. (I'm not really interested in measure theory on its own.)

Answer: 
I suggest [A first look at rigorous probability](http://rads.stackoverflow.com/amzn/click/9812703713) by Jeffrey Rosenthal.
Although it is little terse, I like Durrett's [Probability: Theory and Examples](http://www.math.duke.edu/~rtd/PTE/pte.html).