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 $n\\in\\mathbb{N}$ .

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