Any idea about this problem:
Let $f:A\subset\mathbb{R}^m \longrightarrow B\subset\mathbb{R}^n$ continuous such that:
$\|f(x)-f(y)\|\ge \alpha\cdot\|x-y\|,\forall x,y\in A$ ($\alpha >0$ is a constant)
If $g:B \longrightarrow \mathbb{R}$ is an Riemann integrable function, prove that $g\circ f:A \longrightarrow \mathbb{R}$ is an Riemann integrable function.
Any hints would be appreciated.