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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A direct proof of Porcelli's condition for weak convergence


Author: R. B. Darst
Journal: Proc. Amer. Math. Soc. 17 (1966), 1094-1096
MSC: Primary 46.20
MathSciNet review: 0206687
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  • [1] S. Banach, Théorie des opérations lineaires, Chelsea, New York, 1955.
  • [2] T. H. Hildebrandt, On a theorem in the space $ {l_1}$ of absolutely convergent sequences with applications to completely additive set functions, Math. Research Center Rep. No. 62, Madison, Wis., 1958.
  • [3] Shizuo Kakutani, Concrete representation of abstract (𝐿)-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523–537. MR 0004095 (2,318d)
  • [4] Solomon Leader, The theory of 𝐿^{𝑝}-spaces for finitely additive set functions, Ann. of Math. (2) 58 (1953), 528–543. MR 0058126 (15,326b)
  • [5] P. Porcelli, On weak convergence in the space of functions of bounded variation, Math. Research Center Rep. No. 39, Madison, Wis., 1958.
  • [6] -, On weak convergence in the space of functions of bounded variation. II, Math. Research Center Rep. No. 68, Madison, Wis., 1958.
  • [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 0124723 (23 #A2034)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1966-0206687-0
PII: S 0002-9939(1966)0206687-0
Article copyright: © Copyright 1966 American Mathematical Society