Let $\mathbb{R}^d$ be a D816: Euclidean real Cartesian product.
Let $\mu^*$ be the D780: Lebesgue outer measure on $\mathbb{R}^d$.

Then \begin{equation} \forall \, E \subseteq \mathbb{R}^d : \forall \, x \in \mathbb{R}^d : \mu^*(E + x) = \mu^*(E) \end{equation}