Letf(x,y),0≤ x, y ≤ 1,satisfythefollowing conditions: for each x, f(x,y) is an integrable function of y,and(∂f(x,y)/∂x) is a bounded function of (x, y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and d dx 1 0 1 f (x, y)dy = 0 ∂ ∂x f(x,y)dy.
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Letf(x,y),0≤ x, y ≤ 1,satisfythefollowing conditions: for each x, f(x,y) is an integrable function of y,and(∂f(x,y)/∂x) is a bounded function of (x, y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and d dx 1 0 ...