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The Vitali-Hahn-Saks and Nikodym theorems for additive set functions


Author: R. B. Darst
Journal: Bull. Amer. Math. Soc. 76 (1970), 1297-1298
MSC (1970): Primary 2813, 2850
DOI: https://doi.org/10.1090/S0002-9904-1970-12647-7
Part II: Bull. Amer. Math. Soc., Volume 79, Number 4 (1973), 758--760
MathSciNet review: 0264026
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  • 1. James K. Brooks, On the Hahn- Vitali-Saks and Nikodym Theorems, Proc. Nat. Acad. Sci. U.S.A. 64 (1969), 468-471. MR 268343
  • 2. R. 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. MR 25 #1256. MR 137807
  • 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. MR 38 #6360. MR 238084
  • 4. R. B. Darst, A direct proof of Porcelli's condition for weak convergence, Proc. Amer. Math. Soc. 17 (1966), 1094-1096. MR 34 #6505. MR 206687
  • 5. S. Kakutani, Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523-537. MR 2, 318. MR 4095
  • 6. Soloman Leader, The theory of L, Ann. of Math. (2) 58 (1953), 528-543. MR 15, 326. MR 58126
  • 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. MR 23 #A2034. MR 124723

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DOI: https://doi.org/10.1090/S0002-9904-1970-12647-7

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