On the strong law of large numbers for Banach-valued weakly integrable random variables

Zoran R. POP-STOJANOVIC

doi:10.2969/jmsj/02320269

Zoran R. POP-STOJANOVIC

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ジャーナルフリー

1971 年 23 巻 2 号 p. 269-277

DOI https://doi.org/10.2969/jmsj/02320269

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Published: 1971 Received: 1970/03/20 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. Beck, On the strong law of large numbers, Ergodic Theory (ed. F. B. Wright, Academic Press, New York, 1963).
2) J. K. Brooks, Representations of weak and strong integrals in Banach spaces, Proc. Nat. Acad. Sci., U.S.A., 63(2) (1969), 266-270.
3) M. M. Day, Normed linear spaces, Springer-Verlag, Berlin, 1958.
4) J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
5) A. Dvoretzky and C. A. Rogers, Absolute and unconditional convergence in normed spaces, Proc. Nat. Acad. Sci., U.S.A., 36 (1950), 192-197.
6) I. Gelfand, Sur une lemme de la théorie des espaces linéaires, Comm. Inst. Sci., Math. de Kharkoff (4) 13(1936), 35-40.
7) P. Halmos, Measure Theory, Van Nostrand, 1952.
8) E. Hille and R. S. Phillips, Functional Analysis and semi-groups, Colloq. Publ. Amer. Math. Soc., 1957.
9) S. Karlin, Unconditional convergence in Banach spaces, Bull. Amer. Math. Soc., 54 (1948), 148-152.
10) E. Mourier, Elements aléatoires dans un espace de Banach, Gauthier-Villars, Paris, 1954.
11) J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden Day, 1965.
12) B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc., 44 (1938), 277-304.

Right : [1] A. Beck, On the strong law of large numbers, Ergodic Theory (ed. F. B. Wright, Academic Press, New York, 1963).
[2] J. K. Brooks, Representations of weak and strong integrals in Banach spaces, Proc. Nat. Acad. Sci., U. S. A., 63 (2) (1969), 266-270.
[3] M. M. Day, Normed linear spaces, Springer-Verlag, Berlin, 1958.
[4] J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
[5] A. Dvoretzky and C. A. Rogers, Absolute and unconditional convergence in normed spaces, Proc. Nat. Acad. Sci., U. S. A., 36 (1950), 192-197.
[6] I. Gelfand, Sur une lemme de la théorie des espaces linéaires, Comm. Inst. Sci., Math. de Kharkoff (4) 13 (1936), 35-40.
[7] P. Halmos, Measure Theory, Van Nostrand, 1952.
[8] E. Hille and R. S. Phillips, Functional Analysis and semi-groups, Colloq. Publ. Amer. Math. Soc., 1957.
[9] S. Karlin, Unconditional convergence in Banach spaces, Bull. Amer. Math. Soc., 54 (1948), 148-152.
[10] E. Mourier, Elements aléatoires dans un espace de Banach, Gauthier-Villars, Paris, 1954.
[11] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden Day, 1965.
[12] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc., 44 (1938), 277-304.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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