ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4697 on D1746: Simple integral
Simple integral of a measurable simple function 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) $\phi : X \to [0, \infty]$ is a D2956: Measurable simple complex function on $M$
Then \begin{equation} \int_X \phi \, d \delta_{x_0} = \phi(x_0) \end{equation}