# Evaluation functional

## In words...

For a space of real-valued functions over a given domain, the evaluation functional is the functional that, for any function of the space and any point in the domain, outputs the value of the function at that point.

## In pictures...

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## In maths...

The evaluation functional in a space $\H$ of functions from $\X$ to $\Y$ (i.e., $\H\subseteq \Y^\X$) is the functional defined as
$$
e : \X \times \H \rightarrow \Y
$$
with
$$
\forall \g x \in \X,\ \forall f\in\H,\quad e_{\g x}(f) = f(\g x) .
$$