Geodesic
On limit theorems for sums of independent compact random subsets of Euclidean space
Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 113-128

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In the paper an asymptotical behaviour of normed sums of independent random compacts in $R^m$ is investigated. The article contains different convergence conditions for random set series, analogs of the central limit theorem and the strong law of large numbers. 
@article{ZNSL_1979_85_a8,
     author = {N. N. Ljashenko},
     title = {On limit theorems for sums of independent compact random subsets of {Euclidean} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--128},
     publisher = {mathdoc},
     volume = {85},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a8/}
}
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N. N. Ljashenko. On limit theorems for sums of independent compact random subsets of Euclidean space. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 113-128. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a8/