Limit theorems for unions of random sets under multiplicative normalization

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.