NOTE 1 A function D(x) can be considered as a distribution D assigning to a function f(x) the value

$D(f)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}D(x)f(x)\text{d<mi>x</mi>}}$ if this integral exists.

NOTE 2 The derivative of a distribution D is another distribution D′ defined for any function f(x) by

$D^{\prime }(f)=-D(\text{d}f/\text{d}x)$.