Simple function (measure theory)/Definition
From Maths
Definition
A simple function [ilmath]f:X\rightarrow\mathbb{R} [/ilmath] on a measurable space [ilmath](X,\mathcal{A})[/ilmath] is a[1]:
- function of the form [ilmath]\sum^N_{i=1}x_i\mathbf{1}_{A_i}(x)[/ilmath] for
- finitely many sets, [ilmath]A_1,\ldots,A_N\in\mathcal{A} [/ilmath] and
- finitely many [ilmath]x_1,\ldots,x_n\in\mathbb{R} [/ilmath]
