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**sitho** Hi! Just out of curiosity, I've been interested in a kind of function $\displaystyle f:\mathbb{R}\rightarrow\mathbb{R}$ with the properties that it's constant valued, but infinitesimally small everywhere in the real domain, and with finite valued integral over its domain. There are many ways to define this function, one being as a box function:

$\displaystyle f(x) \equiv \lim_{w\to\infty}h(x;w) = \left\lbrace\begin{matrix}\frac{1}{2w} &: |x| \leq w\\0 &: |x|>w\end{matrix}\right.$

Is there a name for this function, and what are its potential applications? I suppose it's similar in concept to the Dirac delta function (one definition of the Dirac delta would be simply to take the limit w to 0 in the above definition).