Let $M = (\mathbb{R}, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that
| (i) | $f : \mathbb{R} \to [0, \infty]$ is a D5610: Unsigned basic Borel function on $M$ |
| (ii) | $a \in \mathbb{R} \setminus \{ 0 \}$ is a D993: Real number |
Then
| (1) | \begin{equation} \int_{\mathbb{R}} f(x / a) \, \ell(d x) = |a| \int_{\mathbb{R}} f(x) \, \ell(d x) \end{equation} |
| (2) | \begin{equation} \int_{\mathbb{R}} f(a x) \, \ell (d x) = \frac{1}{|a|} \int_{\mathbb{R}} f(x) \, \ell(d x) \end{equation} |