Simple function

Let \((X,\mcm)\) be a measurable space. A simple function on \(X\) is a function \(s\colon X\to\CC\) of the form \[ s(x) = \sum_{j=1}^n c_j \chi_{E_j}(x), \] where \(n\geq 1\), \(c_1,\ldots,c_n\in\CC\), \(E_1,\ldots,E_n\in\mcm\), and \(\chi_E\) is the indicator function of \(E\).