Let $M = (\mathbb{R}^N, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that

(i)	$f : \mathbb{R}^N \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$

Let $\lambda \in \mathbb{R} \setminus \{ 0 \}$ be a D993: Real number.

Then

(1)	\begin{equation} \int_{\mathbb{R}^N} f(x / \lambda) \, \mu(d x) = |\lambda|^N \int_{\mathbb{R}^N} f(x) \, \mu(d x) \end{equation}
(2)	\begin{equation} \int_{\mathbb{R}^N} f(\lambda x) \, \mu(d x) = \left| \frac{1}{\lambda} \right|^N \int_{\mathbb{R}^N} f(x) \, \mu(d x) \end{equation}