Hi,
I've had glances at this book. It looks interesting. I even planned to borrow it in order to learn again measure theory (since I don't think I learnt seriously lol). What I like in it, and what should fit for you, is that there are parts in almost every chapter that explain how what you've just been reading about measure theory will relate to probability.
Well, it's worth trying in my opinion 
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shinhidora production
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