1 show that the conclusion of egroffs theorem can, Mathematics

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1 show that the conclusion of egroffs theorem can

(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite.

(2) Extend the Lusin's Theorem to the case when the measure of the domain E is not finite. (Note that we proved in class the Theorem for E with finite measure).

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