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.
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.
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 $k$