If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:
A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015. (MathSciNet review).
This is a great collection of problems with complete solutions.
However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book
W. P. Ziemer, Weakly Differentiable Functions Springer 1989
presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.
