Dirac delta function

In mathematics, the Dirac delta function, is a generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.
A discrete probability distribution is often represented as a generalized probability density function involving Dirac delta functions, which substantially unifies the treatment of continuous and discrete distributions. This is especially useful when dealing with probability distributions involving both a continuous and a discrete part.

The Dirac delta function as the limit (in the sense of distributions) of the sequence of zero-centered normal distributions

The Dirac delta function as the limit (in the sense of distributions) of the sequence of zero-centered normal distributions

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