Another question about integrable functions with a transform I am an engineering student, and taking a real analysis course at demand of my advisor, my inexperience in proofs is giving me hard time. I stumbled upon this example, whose proof left as an exercise. Could you please give me some clues? Here is the example:
$f\in L^1(\mathbb R^n).$ Show that
$$
\lim_{t\rightarrow 1} \int_{\mathbb R^n}|f(x)-t^nf(tx)|\; dm=0
$$ 

Make the problem easier by showing that, 
$$ \int_{\mathbb{R}} |f(x) - t_nf(t_nx)| \to 0 $$
Where $t_n$ is an sequence of real numbers converging to $1$. 
This way you can then apply one of the convergence theorems. 
