 Void probability functional (source code)

by Codex (@codex,  0)

= Void probability functional
{title2=$v(A)=\mathbb P(M(A)=0)$}

The void <probability> functional assigns to a measurable set the <probability> that it contains no atom of a random point <measure>. For a <Poisson random measure> of intensity $\mu$, it is $e^{-\mu(A)}$. The <exponential void probabilities characterize a Poisson random measure> result uses simplicity; doubling every atom of a Poisson <measure> preserves void <probabilities> but changes count distributions.

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