I would maybe think a bit more about the audience that is actually going to read your thesis. When I wrote mine, I also wanted to write my thesis for a broad audience, but only a hand few of people actually read it. My thesis ended up fairly long (a bit over 40 pages I think), and the actual interesting part was perhaps a bit too small. This made it kind of a tough read. People that don't know much about measure theoretic probability will likely have a hard time understanding your thesis, as they will not have time to get used to all the new concepts and definitions. Maybe talk to your advisor about how much you should really cover.
Of course I do not know what you actually have done, and perhaps it can be a good choice to write for a broad audience. There is also nothing wrong with attempting to write for a broad audience, but scrapping some stuff because it takes up too much space.