つづき So, the trick seems to be that we can't expect probability to be σ-additive and to measure the probability of every event, at the same time (which seems really similar to Vitali's and Banach-Tarski's arguments). This explanation makes quite sense to me, but I can't fully understand it. How is the event Ej formally defined? And how is Tao precisely using Fubini's theorem in order to get to a contradiction? Could someone give me a formal definition of Ej and a formal proof which shows that, for every j∈N, Ej is not measurable?
