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Assume f : [a, b] → R is integrable. (a) Show that if g satisfies g(x)...

Assume f : [a, b] → R is integrable. (a) Show that if g satisfies g(x) = f(x) for all but a finite number of points in [a, b], then g is integrable as well. (b) Find an example to show that g may fail to be integrable if it differs from f at a countable number of points.

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