The first

Write down the proof of the Lebesgue-Radon-Nikodym theorem. Include all the details (except for the \(\sigma\)-finite part, for which you may just provide the idea). In other words, go through the proof presented in class, read it carefully, understand the main steps, and fill in the holes in the argument. These missing parts were in fact some of the exercises from last week. After you hand me in your writing, I will post here my own completed proof.

The second

Write down carefully the solutions to problems 9 and 10 of homework 8. The goal is to practise the moment method in the proof of the law of large numbers.