Tao-II: 8.2.7, 8.2.9, 8.2.10

Next week, we are going to consider Fubini's theorem in Tao 8.5 (see also Pugh section 6.7). You can read ahead. You may want to review the fact that, if a non-negative series is convergent, then any rearrangement of the series is convergent (the partial sum will form a monotone bounded sequence), hence a 'double series' of non-negative terms $\sum_n \sum_m a_{nm} = \sum_m \sum_n a_{nm} = \sum_{N=0}^\infty \sum_{n+m=N} a_{nm}$.