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The Vitali-Hahn-Saks and Nikodym theorems for additive set functions. (English) Zbl 0202.33802


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[1] James K. Brooks, On the Vitali-Hahn-Saks and Nikodým theorems, Proc. Nat. Acad. Sci. U.S.A. 64 (1969), 468 – 471. · Zbl 0188.35604
[2] Richard B. Darst, A decomposition for complete normed abelian groups with applications to spaces of additive set functions, Trans. Amer. Math. Soc. 103 (1962), 549 – 558. · Zbl 0112.03703
[3] R. B. Darst, On a theorem of Nikodym with applications to weak convergence and von Neumann algebras, Pacific J. Math. 23 (1967), 473 – 477. · Zbl 0189.44901
[4] R. B. Darst, A direct proof of Porcelli’s condition for weak convergence, Proc. Amer. Math. Soc. 17 (1966), 1094 – 1096. · Zbl 0178.17204
[5] Shizuo Kakutani, Concrete representation of abstract (\?)-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523 – 537. · Zbl 0027.11102 · doi:10.2307/1968915
[6] Solomon Leader, The theory of \?^{\?}-spaces for finitely additive set functions, Ann. of Math. (2) 58 (1953), 528 – 543. · Zbl 0052.11401 · doi:10.2307/1969752
[7] Pasquale Porcelli, Two embedding theorems with applications to weak convergence and compactness in spaces of additive type functions, J. Math. Mech. 9 (1960), 273 – 292. · Zbl 0090.32704
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