Surfing the Internet, looking for something in probability, I found this tutorial: a measure theoretical approach easy to work through. The tutorial is divided by chapters, the explanations are simple and almost all the proofs are left to the student, but they are easily induced given the way the text is constructed.
Apparently, the idea of the author was to introduce a complete tutorial in probability topics, including other aspects –not only the formal theory, but maybe he was absorbed by other projects.
I have not seen the complete material but what I read seems to be well written. Enjoy it!