Geodesic
On Minkowski Sums of Many Small Sets
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 88-91

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It is proved that a weakly closed subset of a Banach space is convex if and only if it can be represented as the sum of sets of arbitrarily small diameter.
Keywords: Minkowski addition, infinite divisibility, weak compactness, convexity. 
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     author = {M. M. Roginskaya and V. S. Shul'man},
     title = {On {Minkowski} {Sums} of {Many} {Small} {Sets}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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M. M. Roginskaya; V. S. Shul'man. On Minkowski Sums of Many Small Sets. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 88-91. http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a8/