# Meaning of Point Evaluation

I read in some general measure theory books and there is always like "define measure $x$ to be the point evaluation at $y$..." but when I look around online and some other books there is no mention on what is "point evaluation". Can anyone explain to me what is point evaluation?

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Could it mean that the measure of a set $A$ is 1 if $y\in A$, and 0 otherwise? –  Hagen von Eitzen Sep 2 '12 at 18:45

$$\int_X f(x) \, d \mu = f(y)$$
(evaluation at the point $y$).
In other words, we're thinking of the measure as corresponding to a linear functional on some space of functions, and so "point evaluation at $y$" refers to the linear functional $f \to f(y)$. –  Robert Israel Sep 2 '12 at 19:25