Geodesic
The continuity of semiadditive functionals
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 541-548 
E. I. Smirnov. The continuity of semiadditive functionals. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 541-548. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a6/
@article{MZM_1976_19_4_a6,
     author = {E. I. Smirnov},
     title = {The continuity of semiadditive functionals},
     journal = {Matemati\v{c}eskie zametki},
     pages = {541--548},
     year = {1976},
     volume = {19},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we examine a general principle of continuity of semiadditive functionals on a metric linear space (MLS) that extends various results obtained previously in this respect. In particular, from our fundamental Theorem 1 it is easy to obtain Banach's closed graph theorem, the Banach–Steinhaus theorem, the weak base theorem, and others.