Completeness of $L_1$ spaces over finitely additive probabilities

• Autorzy: S. Gangopadhyay , B. V. Rao
• Języki publikacji: EN

Słowa kluczowe

EN

Sobczyk-Hammer decomposition; Hewitt-Yosida decomposition; $L_1$ space; strategic products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 83-95

Daty

wydano

1999

otrzymano

1998-01-05

poprawiono

1998-08-26

Twórcy

autor

S. Gangopadhyay

• Stat-Math Division, Indian Statistical Institute, 203, B.T. Road, Calcutta 700035, India

autor

B. V. Rao

• Stat-Math Division, Indian Statistical Institute, 203, B.T. Road, Calcutta 700035, India

Bibliografia

• [1] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges--a Study of Finitely Additive Measures, Academic Press, 1983.
• [2] R. Chen, A finitely additive version of Kolmogorov's law of iterated logarithm, Israel J. Math. 23 (1976), 209-220.
• [3] R. Chen, Some finitely additive versions of the strong law of large numbers, ibid. 24 (1976), 244-259.
• [4] L. E. Dubins and L. J. Savage, How to Gamble if You Must: Inequalities for Stochastic Processes, McGraw-Hill, 1965.
• [5] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, 1958.
• [6] S. Gangopadhyay, On the completeness of $\cal L_p$-spaces over a charge, Colloq. Math. 58 (1990), 291-300.
• [7] S. Gangopadhyay and B. V. Rao, Some finitely additive probability: random walks, J. Theoret. Probab. 10 (1997), 643-657.
• [8] S. Gangopadhyay and B. V. Rao, Strategic purely nonatomic random walks, ibid. 11 (1998), 409-415.
• [9] S. Gangopadhyay and B. V. Rao, On the Hewitt-Savage zero one law in the strategic setup, preprint.
• [10] J. W. Hagood, A Radon-Nikodym theorem and $L_p$ completeness for finitely additive vector measures, J. Math. Anal. App. 113 (1986), 266-279.
• [11] A. Halevy and M. Bhaskara Rao, On an analogue of Komlos' theorem for strategies, Ann. Probab. 7 (1979), 1073-1077.
• [12] D. Heath and W. D. Sudderth, On finitely additive priors$,$ coherence$,$ and extended admissibility, Ann. Statist. 6 (1978), 333-345.
• [13] D. Heath and W. D. Sudderth, Coherent inference from improper priors and from finitely additive priors, ibid. 17 (1989), 907-919.
• [14] E. Hewitt and L. J. Savage, Symmetric measures on Cartesian products, Trans. Amer. Math. Soc. 80 (1955), 470-501.
• [15] R. L. Karandikar, A general principle for limit theorems in finitely additive probability, ibid. 273 (1982), 541-550.
• [16] R. L. Karandikar, A general principle for limit theorems in finitely additive probability$:$ the dependent case, J. Multivariate Anal. 24 (1988), 189-206.
• [17] D. A. Lane and W. D. Sudderth, Diffuse models for sampling and predictive inference, Ann. Statist. 6 (1978), 1318-1336.
• [18] R. A. Purves and W. D. Sudderth, Some finitely additive probability, Ann. Probab. 4 (1976), 259-276.
• [19] R. A. Purves and W. D. Sudderth, Finitely additive zero-one laws, Sankhyā Ser. A 45 (1983), 32-37.
• [20] S. Ramakrishnan, Finitely additive Markov chains, Ph.D. thesis, Indian Statistical Institute, 1980.
• [21] S. Ramakrishnan, Finitely additive Markov chains, Trans. Amer. Math. Soc. 265 (1981), 247-272.
• [22] S. Ramakrishnan, Central limit theorem in a finitely additive setting, Illinois J. Math. 28 (1984), 139-161.
• [23] S. Ramakrishnan, Potential theory for finitely additive Markov chains, Stochastic Process. Appl. 16 (1984), 287-303.
• [24] R. Ranga Rao, A note on finitely additive measures, Sankhyā Ser. A 18 (1958), 27-28.
• [25] A. Sobczyk and P. C. Hammer, A decomposition of additive set functions, Duke Math. J. 11 (1944), 839-846.
• [26] K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66.