Does there exist a generalization of Egoroff theorem for nets instead of sequences of functions?

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Does there exist a generalization of Egoroff theorem for nets instead of sequences of functions?

expectany very useful extension: the reason that measure theory plays so well with sequences is that both of them privilege countability (the first in terms of what sort of additivity we have, and the second in terms of the indexing set). $\endgroup$ – LSpice Aug 19 '18 at 18:34