Formulation on R2966: Indicator function under scaling of the argument
Formulation 0
Let $\mathbb{R}^N$ be a D816: Euclidean real Cartesian product such that
(i) $E \subseteq \mathbb{R}^N$
(ii) $I_E$ is an D41: Indicator function on $\mathbb{R}^N$ with respect to $E$
(iii) $x \in \mathbb{R}^N$
Let $a \in \mathbb{R}$ be a D993: Basic real number such that
(i) \begin{equation} a \neq 0 \end{equation}
(1) \begin{equation} I_E(a x) = I_{a^{-1} E} (x) \end{equation}
(2) \begin{equation} I_E (a^{-1} x) = I_{a E} (x) \end{equation}