Dirac delta distribution

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{- \infty}^{\infty} f(x) \delta (x-a) dx = f(a)}