Hi, this is not a homework problem because as you can see, all schools are closed for the winter break. But I'm currently working on a problem and I'm not sure how to begin to attack it. Here's the entire problem:(adsbygoogle = window.adsbygoogle || []).push({});

Let f be bounded and measurable function on [0,00). For x greater than or equal to 0, define F(x)= \int_{0,...,x} f(t)dt.

Part i. Show that there is some positive M such that |F(x)-F(y)| <= M|x-y|.

Part ii. Prove that there exist a constant C such that m(F(E)) <= C(m(E)) for every Lebesgue measurable set E of [0,00). Note that m(E) is the Lebesgue measure of the set E and F(E) := {F(x) : x is in E}.

I know how to do Part i. But as for Part ii., I'm not sure how to begin working on it. Can I rewrite E as an infinite disjoint union of open/closed sets??

Note that 00 means infinity and <= means less than or equal to.

Thank you.

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