= Existence of a Poisson random measure on a standard Borel space
A <sigma-finite measure> on a <standard Borel space> is the <intensity measure of a point process> with Poisson counts. Partition the space into sets of finite intensity, draw an independent Poisson count on each piece, and conditional on that count draw independent points from its normalized intensity measure. The sum of their <Dirac measures> is the required <Poisson random measure>. Non-atomic intensity gives simplicity; local finiteness of the intensity gives local finiteness of the point configuration.
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