This appears in Grafakos book Lorentz spaces? How to prove $d_{\delta^{\epsilon}(f)}(\alpha)=\epsilon^{-n}d_{f}(\alpha)$? where $\delta^{\epsilon}(f)(x)=f(\epsilon x)$,$d_{g}(\alpha)=\mu\{x:|g(x)|>\alpha\}$ and $\mu$ is the Lebesgue measure.
By definition we have $d_{\delta^{\epsilon}(f)}(\alpha)=\mu\{x:|\delta^{\epsilon}(f)|>\alpha\}=\mu\{x:|f(\epsilon x)|>\alpha\}=\int_{\mathbb{R}^{n}}\chi_{\{x:|f(\epsilon x)|>\alpha\}}dx$ How to transformation? Any hints are wellcome!!!