We define a general notion of "summability" of a set $I\subseteq\mathbb{C^{N}}$ and show that some trivial condition necessary for a set to be summable, is also sufficient. We deduce some intresting corollaries.
Summability of multilinear mappings: Littlewood, Orlicz and beyond
Direct sums and summability of the Szlenk index
Estimating the index of summability of pairs of Banach spaces
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