§4.4 Step Functions and Regulated Functions
Solomon Leader · 2001
Theorem 1. (Step Functions.) For g a function on a cell K the following conditions are equivalent: (i) g is a a step function. (That is, (1) holds.) (ii) K is a finite union of disjoint intervals / i , · · · , In (some of which may be degenerate) such that g is constant on each Ii.