Definition 18.4.2 (Indicator Function).label Let $E$ be a vector space over $\real$ and $A \subset E$, then the mapping
\[I_{A}: E \to (-\infty, \infty] \quad x \mapsto \begin{cases}\infty &x \not\in A \\ 0 & x \in A\end{cases}\]
is the infinity characteristic function/indicator function of $A$.
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