ThmDex – An index of mathematical definitions, results, and conjectures.
Unsigned basic integral with respect to a point measure
Formulation 0
Let $M = (X, \mathcal{F}, \delta_{x_0})$ be a D5671: Point measure space such that
(i) $f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$
Then \begin{equation} \int_X f \, d \delta_{x_0} = f(x_0) \end{equation}