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Reference.org
Mapping theorem (point process)
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<p>The mapping theorem is a theorem in the theory of <a href="/facts/Point_process/zsJmxmFf">point processes</a>, a sub-discipline of <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>. It describes how a <a href="/facts/Poisson_point_process/8uphjAUc">Poisson point process</a> is altered under <a href="/facts/Measurable_function/NgIHnb1b">measurable transformations</a>. This allows construction of more complex Poisson point processes out of <a href="/facts/Homogeneous_Poisson_point_process/8uphjAUc">homogeneous Poisson point processes</a> and can, for example, be used to simulate these more complex Poisson point processes in a similar manner to <a href="/facts/Inverse_transform_sampling/fIDxBxT6">inverse transform sampling</a>. </p>