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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2018_52_3_a8,
     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},
     pages = {88--91},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a8/}
}
TY  - JOUR
AU  - M. M. Roginskaya
AU  - V. S. Shul'man
TI  - On Minkowski Sums of Many Small Sets
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2018
SP  - 88
EP  - 91
VL  - 52
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a8/
LA  - ru
ID  - FAA_2018_52_3_a8
ER  - 
%0 Journal Article
%A M. M. Roginskaya
%A V. S. Shul'man
%T On Minkowski Sums of Many Small Sets
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2018
%P 88-91
%V 52
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a8/
%G ru
%F FAA_2018_52_3_a8
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/

[1] V. Kreinovich, Reliab. Comput., 1:1 (1995), 33–40 | DOI | MR | Zbl

[2] T. Tao, V. H. Vu, Additive Combinatorics, Cambridge Univ. Press, Cambridge, 2006 | MR | Zbl

[3] J.-M. Deshouillers et al (eds.), Structure Theory of Set Addition, Asterisque, 258, Soc. Math. France, Paris, 1999 | Zbl

[4] M. B. Nathanson, Additive Number Theory. Inverse Problems and Geometry of Sumsets, Springer-Verlag, New York, 1996 | MR | Zbl

[5] D. H. Hyers, Proc. Nat. Acad. Sci USA, 27 (1941), 222–224 | DOI | MR