Question: Show that if f is integrable, there exist continuous, integrable functions g , such that g (x) - f(x) except on a set of Lebesgue

Show that if f is integrable, there exist continuous, integrable functions g , such that g (x) - f(x) except on a set of Lebesgue measure 0. (Use Theorem 17.1(ii) with ( = n~2.)Theorem 17.1. Suppose that fIf| dx 0. (i) There is a step function 8 = Et_, x; IA, with bounded intervals as the A;, such that fIf - 8| dx

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