A direct proof of Porcelli’s condition for weak convergence
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- by R. B. Darst
- Proc. Amer. Math. Soc. 17 (1966), 1094-1096
- DOI: https://doi.org/10.1090/S0002-9939-1966-0206687-0
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References
- S. Banach, Théorie des opérations lineaires, Chelsea, New York, 1955.
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.
- Shizuo Kakutani, Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523–537. MR 4095, DOI 10.2307/1968915
- Solomon Leader, The theory of $L^p$-spaces for finitely additive set functions, Ann. of Math. (2) 58 (1953), 528–543. MR 58126, DOI 10.2307/1969752 P. Porcelli, On weak convergence in the space of functions of bounded variation, Math. Research Center Rep. No. 39, Madison, Wis., 1958. —, On weak convergence in the space of functions of bounded variation. II, Math. Research Center Rep. No. 68, Madison, Wis., 1958.
- 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, DOI 10.1512/iumj.1960.9.59016
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 17 (1966), 1094-1096
- MSC: Primary 46.20
- DOI: https://doi.org/10.1090/S0002-9939-1966-0206687-0
- MathSciNet review: 0206687