Exercises
[0FZ]Let \(I\) be a family of indices, let \(a_ i\) be a sequence with \(a_ iβ₯ 0\); let moreover \(\mathcal F\) be a partition of \(I\) (not necessarily of finite cardinality); then prove that
\[ β_{Fβ\mathcal F}β_{iβ F} a_ i = β_{iβ I} a_ i\quad . \]