Let I {\displaystyle {}I} be a real interval with endpoints a , b ∈ R {\displaystyle {}a,b\in \mathbb {R} } , and let
denote a step function for the partition a = a 0 < a 1 < a 2 < ⋯ < a n − 1 < a n = b {\displaystyle {}a=a_{0}<a_{1}<a_{2}<\cdots <a_{n-1}<a_{n}=b} , with the values t i {\displaystyle {}t_{i}} , i = 1 , … , n {\displaystyle {}i=1,\ldots ,n} . Then
is called the step integral of t {\displaystyle {}t} on I {\displaystyle {}I} .