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Please help me to do the following problem...

For $k>0$ and $A$ is a subset of $\mathbb R$,let $kA=\{kx:x∈A\}$

Show that $m^{*}(kA)=k m^{*}(A)$ $A$ is measurable if and only if $kA$ is measurable.

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    It is true for intervals. Use the definition of outer measure.2012-11-20

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Consider the function $f(x)=x/k$. f is measurale therefore $kA=f^{-1}(A)$ is also measurable.

Now repeat the same argument using the inverse of $k$