Geodesic
Sequences of closed sets of bounded variation converging in the deviation metric
Matematičeskie zametki, Tome 15 (1974) no. 4, pp. 521-526.

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From an arbitrary convergent sequence of sets of bounded variation we can select a subsequence such that there is convergence in almost every hyperplane. 
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     author = {V. S. Meilanov},
     title = {Sequences of closed sets of bounded variation converging in the deviation metric},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1974},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_4_a1/}
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V. S. Meilanov. Sequences of closed sets of bounded variation converging in the deviation metric. Matematičeskie zametki, Tome 15 (1974) no. 4, pp. 521-526. http://geodesic.mathdoc.fr/item/MZM_1974_15_4_a1/