A function on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a, b)⊆R. Therefore, a step function f can be written as f(x) = α_1 f_1(x) + ... + α_n f_n(x), where α_i element R, f_i(x) = 1 if x element [a_i, b_i) and 0 otherwise, for i = 1, ..., n.