stair function

A stair function is a real function of the form

$$\varphi =\sum _{k=1}^n{a}_k{\chi }_{I_k}$$ (1)

where  $a_k\in ℝ$,  ${\chi }_{I_k}$ is the characteristic function, $k=1,2,\mathrm{\dots },n$ and $I_1,I_2,\mathrm{\dots }{I}_n$ are bounded, pairwise disjoint intervals, for some $n\in \mathbb{N}$.

Title	stair function
Canonical name	StairFunction
Date of creation	2013-03-22 15:32:32
Last modified on	2013-03-22 15:32:32
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	6
Author	georgiosl (7242)
Entry type	Definition
Classification	msc 26-00