EDB — 0FZ

Exercises

1. [0FZ]Let \(I\) be a family of indices, let \(a_ i\) be a sequence with \(a_ i≥ 0\); let moreover \(\mathcal F\) be a partition of \(I\) (not necessarily of finite cardinality); then prove that

   \[ ∑_{F∈\mathcal F}∑_{i∈ F} a_ i = ∑_{i∈ I} a_ i\quad . \]