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Let f be monotone increasing and absolutely continuous on [0, 1]. Let E be a subset...

Let f be monotone increasing and absolutely continuous on [0, 1]. Let E be a subset of [0, 1] with m∗(E) = 0. Show that m∗(f(E)) = 0. Hint: cover E with countably many intervals of small total length and consider what f does to those intervals. Use Vitali Covering Argument

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