## Limit theorems for unions of random closed sets |

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### Contents

Distributions of Random Closed Sets | 1 |

Multivalued Regularly Varying Functions and Their Application | 6 |

Survey on Stability of Random Sets and Limit Theorems | 15 |

Copyright | |

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### Common terms and phrases

a-lXn an(K Aumann expectation belonging Boolean model capacity functional Choquet capacity coincides compact sets conditions of Theorem consider convergence of random converges weakly convex compact convex hulls convex random convex sets Corollary corresponding defined Denote easy to show equal EXAMPLE fixed points Galambos Gine half-spaces Hausdorff metric Hence homogeneous hulls of random iid random inclusion functional large numbers law of large Lebesgue measure Lemma Let F limit theorems limiting random set Matheron Minkowski addition Minkowski sums Molchanov multivalued function non-random Norberg Note pointwise convergence Poisson point process probability metrics random closed set random variables random vector regular variation regularly varying function Section 1.6 sequence Stoyan strictly C-stable sufficiently large support function Suppose Theorem 4.1 theorems for unions tk(x Tn(K TX(K TY(K U-stable random set U-stable sets union-infinitely-divisible union-stable unions of random valid weak convergence yields