Does anyone have any advice as to what measure-theoretic Probability Theory books there are with lots of worked examples? I know that measure-theoretic probability book reference requests have been mentioned quite a few times on this site. However, I was wondering if anyone knew of any good books out there with lots of worked examples that go in a step-by-step fashion. One example I am talking about would be the Schaum's worked example series. I would like to solve as many problems as I can and so any reference with lots of worked examples would be a great resource. Thank you in advance and any advice would be greatly appreciated!

The closest books I know with lots of worked exercises on measure-theoretic probability theory are:
"Problems and Solutions in Mathematical Finance: Volume 1 - Stochastic Calculus" by Chin, Nel and Olafsson. As you can see from the title, it contains more than just probability theory, but I think chapter I covers exactly the basics you need, and chapter 2 covers some part of martingale theory. The solutions are very detailed.
Another relevant book (which starts at a little lower level) is "Probability Through Problems" by Capinski and Zastawniak, but it looks like it contains all the basics covered in a first graduate probability class. 
I've also found the book "Problems in Probability" by Shiryaev and Lyasoff, but it doesn't seem to contain step-by-step solutions, just hints. Also, the book "One Thousand Exercises in Probability" by Grimmett and Stirzaker seems to be too low level, as it is not using measure theory.
