nondecreasing rearrangement is equimeasurable

Question

Two functions $f(x)$ and $g(x)$ are called equi-measurable if $m(\{x:f(x)>t\})=m(\{x:g(x)>t\})$. Nondecreasing rearrangement of a function $f(x)$ is defined as $$f^*(\tau)=\inf\{t>0:m(\{x:f(x)>t\}\leq\tau\}.$$ Prove that $f^*(\tau)$ and $f(x)$ are equimeasurable.