## Random Measures |

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apply arbitrary argument assertion assume atoms B E B bounded Chapter choose clearly closed completes conclude condition consider contains continuous convergence Corollary corresponding countable Cox process DC-ring DC-semiring define definition denote determined diffuse directed disjoint distribution easily equals equivalent Exercise exists extends fact Finally finite fixed follows function further given hence Hint holds implies independent infinitely divisible integral intensity introduce KALLENBERG latter Lemma lim sup limit mapping MATTHES means mixed monotone Moreover Note null-array o-finite obtain particular partitions point process positive probability proof proof of Theorem prove random measure random variable relation remains true replaced respectively result satisfying seen sequence Show simple space supporting suppose symmetrically Theorem Theorem 6.1 unique write yields