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Suppose $E$ is a measurable set and $m(E)<+\mathrm{\infty}$. $\{{f}_{k}\}$ is a sequence of non-negative measurable functions. If

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prove that ${f}_{k}$ converge to 0 in measure.

If we can prove $\frac{{f}_{k}(x)}{1+{f}_{k}(x)}\to 0$ a.e.$x\in E$, then the problem is easy to solve. Is it correct? If so, how to prove that?

Appreciate any hint or help!

$$

prove that ${f}_{k}$ converge to 0 in measure.

If we can prove $\frac{{f}_{k}(x)}{1+{f}_{k}(x)}\to 0$ a.e.$x\in E$, then the problem is easy to solve. Is it correct? If so, how to prove that?

Appreciate any hint or help!