Let $f\in L^p(R^d)$ ($p<\infty$) and $\delta_h f(x):=h^{d/p}f(hx)$ (the normalization is so that $\|\delta_h f\|_{p} =\|f\|_p$). Consider $(h_n)$ a sequence of positive numbers such that either $h_n\to0$ or $h_n\to\infty$.
How do I show that $\delta_{h_n}f(x)\to 0$ a.e. $x\in R^d$?
Although I'm not sure is needed, we can assume $p>2$.