The simplest functions you will ever integrate, hence the name.
A measurable function f : X → R {\displaystyle f:X\rightarrow \mathbb {R} } is a simple function if f ( X ) {\displaystyle f(X)} is a finite subset of R {\displaystyle \mathbb {R} } .[1][2] The standard representation for a simple function is given by f ( x ) = ∑ i = 1 n c i 1 E i ( x ) {\displaystyle f(x)=\sum _{i=1}^{n}c_{i}1_{E_{i}}(x)} .
