# stair function

A stair function is a real function of the form

 $\phi=\sum_{k=1}^{n}a_{k}\chi_{I_{k}}$ (1)

where  $a_{k}\in\mathbb{R}$,  $\chi_{I_{k}}$ is the characteristic function, $k=1,2,\ldots,n$ and $I_{1},I_{2},\ldots I_{n}$ are bounded, pairwise disjoint intervals, for some $n\in\mathbb{N}$.

Title stair function StairFunction 2013-03-22 15:32:32 2013-03-22 15:32:32 georgiosl (7242) georgiosl (7242) 6 georgiosl (7242) Definition msc 26-00