Remark 4.7.3.18. Let $\kappa $ and $\lambda $ be infinite cardinals. Then $\kappa \leq \mathrm{ecf}(\lambda )$ if and only if the following condition is satisfied: for every collection of $\lambda $-small sets $\{ T_ s \} _{s \in S}$ indexed by a $\kappa $-small set $S$, the product ${\prod }_{s \in S} T_{s}$ is also $\lambda $-small.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$