Formulation on R2966: Indicator function under scaling of the argument
F8789
Formulation 2
Let $\mathbb{R}^N$ be a D816: Euclidean real Cartesian product.
Let $I_E$ be an D41: Indicator function for $E \subseteq \mathbb{R}^N$ in $\mathbb{R}^N$.
Let $a, x \in \mathbb{R}$ each be a D993: Basic real number such that
(i) $a \neq 0$
Then
(1) \begin{equation} I_E(a x) = I_{\frac{1}{a} E} (x) \end{equation}
(2) \begin{equation} \textstyle I_E (\frac{1}{a} x) = I_{a E} (x) \end{equation}