Generalized Egoroff's theorem

Abstract

This note is closely related to the paper [8] and it presents slight improvements of its results. Theorem 1.13 shows a connection with Galois-Tukey embeddings, Corollary 1.14 presents another inequality which is dual
to the previously known one; Corollary 3.5 shows that there is no distinction between positive outer measure and full outer measure in the given context, and Corollary 4.3 unies the known counterexamples.