Question: =+function g such that A[ x (0, 1): f(x) + g(x)]

=+function g such that A[ x € (0, 1): f(x) + g(x)]<€.

(a) Show that f may be assumed integrable, or even bounded.

(b) Let g ,, be continuous functions converging to f almost everywhere.

Combine Egoroff's theorem and Theorem 12.3 to show that convergence is uniform on a compact set K such that A((0,1) -K)

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