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: 
Although it is a rather thick book I recommend Billingsley's [Probability and Measure](http://rads.stackoverflow.com/amzn/click/0471007102).
How about [www.probability.net](http://www.probability.net) for a nice introduction...