Definition
59
[0FW]Let \(I\) be an infinite family of indices and let \(a_ i:Iβ[0,β]\) be a generalized sequence, we define the sum \(β_{iβ I}a_ i\) as
\[ β_{iβ I}a_ i = \sup \left\{ β_{iβ K}a_ i : Kβ {\mathcal P}_{\mathfrak f}(I) \right\} \]
where \({\mathcal P}_{\mathfrak f}(I)\) is the set of finite subsets \(Kβ I\).