Where the scaling property $\int_{-\infty}^\infty f(ax)dx=\frac1a \int_{-\infty}^\infty f(x)dx$ comes from in the theory of distributions?
Basically, if the distributions are defined as linear maps $f:\psi \in {\mathcal {D}}(\mathbb {R} )\to\int_{-\infty}^\infty f(x)\psi(x)dx\in\mathbb{R}$, where the scaling property comes from? Or it is a separate postulate?