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Heaviside step function
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==Relationship with Dirac delta== The [[Dirac delta function]] is the [[weak derivative]] of the Heaviside function: <math display="block">\delta(x)= \frac{d}{dx} H(x).</math> Hence the Heaviside function can be considered to be the [[integral]] of the Dirac delta function. This is sometimes written as <math display="block">H(x) := \int_{-\infty}^x \delta(s)\,ds</math> although this expansion may not hold (or even make sense) for {{math|''x'' {{=}} 0}}, depending on which formalism one uses to give meaning to integrals involving {{mvar|Ξ΄}}. In this context, the Heaviside function is the [[cumulative distribution function]] of a [[random variable]] which is [[almost surely]] 0. (See [[Constant random variable]].)
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