Geodesic
Limit theorems for unions of random sets under multiplicative normalization
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 638-645

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This paper finds conditions for weak convergence of normalized unions $a_n^{ - 1} (A_1 \cup \ldots A_n )$ of independent and identically distributed random closed sets $A_1 , \ldots ,A_n$ in terms of regular variation of corresponding accompanying functionals. The special case $A_1 = M(\xi )$, where $M$ is a multivalued function and $\xi $ a random vector with regularly varying density is also considered.
Keywords: random closed sets, regularly varying function, capacity, max-stable law. 
@article{TVP_1993_38_3_a13,
     author = {I. S. Molchanov},
     title = {Limit theorems for unions of random sets under multiplicative normalization},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {638--645},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a13/}
}
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I. S. Molchanov. Limit theorems for unions of random sets under multiplicative normalization. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 638-645. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a13/