Old exams from the period 2010–2020 can be found here. Solutions are compiled here. Note that the exam from 2020 is more substantial than previous exams since the exam was available for one week.
Some of the problems may not be relevant to the current curriculum. I have stolen and lightly edited the following description from the 2020 course page.
Exam problems back to and including 2013 are, with a few exceptions, still relevant for the course. Before 2013 the curriculum was substantially different, and I do not recommend working on the problems for the period 2010-12 (if you need more problems, take a look at the mandatory assignments instead, or some of the extra problems that were given in the 2019 version of the course).
After 2012, the only problems outside this years curriculum seem to be problems involving Fubini and Tonelli's theorems on product measures. There are also a few instances of terminology and notation that you are probably not familiar with. Here is what I found (I may have missed a few things!):
Exam 2015: Problem 1 requires Tonelli's Theorem. The notation also differs a little from what we are used to: In Problem 4, \(Im(B)\) denotes the image of the operator \(B\), and \((x|y)\) denotes the inner product of \(x\) and \(y\).
Exam 2014, Problem 2: Requires Fubini's Theorem.
Exam 2013, Problem 1: The space \(l^{\infty}(X)\) is defined slightly differently from what we are used to, but that shouldn't really matter.