Dirac delta distribution

The Dirac delta distribution (or generalized function) is written as $δ(x)$ . It is the derivative of the Heaviside step distribution,

$\frac{d}{dx}[H(x)] = \delta(x)$

It has the property

$\int_{- \infty}^{\infty} f(x) \delta (x-a) dx = f(a)$

[edit] Applications in statistical mechanics