High Quality Content by WIKIPEDIA articles! In probability theory, a random measure is a measure-valued random element. This random measure describes the set of N particles, whose locations are given by the (generally vector valued) random variables Xn. Random measures are useful in the description and analysis of Monte Carlo methods, such as Monte Carlo numerical quadrature and particle filters. In mathematics, a point process is a random element whose values are "point patterns" on a set S. While in the exact mathematical definition a point pattern is specified as a locally finite counting measure, it is sufficient for more applied purposes to think of a point pattern as a countable subset of S that has no limit points.

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