Automorphism induced automorphism of Lp spaces

Question

Let $(\mathbb{R}^d,\mathbb{B}(\mathbb{R}^d),\mu)$ where $\mu$ is a $\sigma$-finite Radon measure. If $\Phi:\mathbb{R}^d\rightarrow \mathbb{R}^d$ is a homeomorphism, then does $\Phi$ induce a homeomorphism of the Bochner-Lebesgue space $L^p_{\mu}(\mathbb{R}^d;\mathbb{R}^d)$ onto itself by $$ f\mapsto \Phi^{-1}\circ f\circ\Phi? $$