Abstract
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.
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Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 541–548, April, 1976.
The author expresses his gratitude to P. P. Zabreiko for his guidance.
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Smirnov, E.I. The continuity of semiadditive functionals. Mathematical Notes of the Academy of Sciences of the USSR 19, 329–333 (1976). https://doi.org/10.1007/BF01156792
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DOI: https://doi.org/10.1007/BF01156792