On a generalization of Egoroff's theorem
Standard techniques are used to prove a slight variation of Egoroff's theorem, namely that if a sequence \(\{f_n\}\) of measurable real valued functions converges on a set \(A\), then the sequence converges almost uniformly on any subset \(B \subseteq A\) of finite measure. A standard example showing the need for finiteness of the measure of \(B\) is presented as well.
scientific article; zbMATH DE number 1605050