If f and g are integrable functions on (X, S, ) and (Y, T, v), respectively,...

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If f and g are integrable functions on (X, S, μ) and (Y, T, v), respectively, and F(x, y) = f(x) g(y), show that F is integrable on X *Y and [Fd(u*v) = integrate fdu integrate gdv. If f and g are integrable functions on (X, S, μ) and (Y, T, v), respectively, and F(x, y) = f(x) g(y), show that F is integrable on X *Y and [Fd(u*v) = integrate fdu integrate gdv.

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