Dirac delta distribution

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The Dirac delta distribution (or generalized function) is written as \delta(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)

Applications in statistical mechanics