Completeness of L 1 spaces over finitely additive probabilities

S. Gangopadhyay; B. Rao

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 1, page 83-95
  • ISSN: 0010-1354

How to cite

top

Gangopadhyay, S., and Rao, B.. "Completeness of $L_1$ spaces over finitely additive probabilities." Colloquium Mathematicae 80.1 (1999): 83-95. <http://eudml.org/doc/210707>.

@article{Gangopadhyay1999,
author = {Gangopadhyay, S., Rao, B.},
journal = {Colloquium Mathematicae},
keywords = {Sobczyk-Hammer decomposition; Hewitt-Yosida decomposition; $L_1$ space; strategic products; finitely additive measure; space; strategic product},
language = {eng},
number = {1},
pages = {83-95},
title = {Completeness of $L_1$ spaces over finitely additive probabilities},
url = {http://eudml.org/doc/210707},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Gangopadhyay, S.
AU - Rao, B.
TI - Completeness of $L_1$ spaces over finitely additive probabilities
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 1
SP - 83
EP - 95
LA - eng
KW - Sobczyk-Hammer decomposition; Hewitt-Yosida decomposition; $L_1$ space; strategic products; finitely additive measure; space; strategic product
UR - http://eudml.org/doc/210707
ER -

References

top
  1. [1] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges--a Study of Finitely Additive Measures, Academic Press, 1983. Zbl0516.28001
  2. [2] R. Chen, A finitely additive version of Kolmogorov's law of iterated logarithm, Israel J. Math. 23 (1976), 209-220. Zbl0367.60027
  3. [3] R. Chen, Some finitely additive versions of the strong law of large numbers, ibid. 24 (1976), 244-259. Zbl0367.60026
  4. [4] L. E. Dubins and L. J. Savage, How to Gamble if You Must: Inequalities for Stochastic Processes, McGraw-Hill, 1965. Zbl0133.41402
  5. [5] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, 1958. 
  6. [6] S. Gangopadhyay, On the completeness of p -spaces over a charge, Colloq. Math. 58 (1990), 291-300. Zbl0719.28002
  7. [7] S. Gangopadhyay and B. V. Rao, Some finitely additive probability: random walks, J. Theoret. Probab. 10 (1997), 643-657. Zbl0886.60001
  8. [8] S. Gangopadhyay and B. V. Rao, Strategic purely nonatomic random walks, ibid. 11 (1998), 409-415. Zbl0914.60039
  9. [9] S. Gangopadhyay and B. V. Rao, On the Hewitt-Savage zero one law in the strategic setup, preprint. Zbl0978.60028
  10. [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. Zbl0601.28005
  11. [11] A. Halevy and M. Bhaskara Rao, On an analogue of Komlos' theorem for strategies, Ann. Probab. 7 (1979), 1073-1077. Zbl0425.60022
  12. [12] D. Heath and W. D. Sudderth, On finitely additive priors , coherence , and extended admissibility, Ann. Statist. 6 (1978), 333-345. Zbl0385.62005
  13. [13] D. Heath and W. D. Sudderth, Coherent inference from improper priors and from finitely additive priors, ibid. 17 (1989), 907-919. Zbl0687.62003
  14. [14] E. Hewitt and L. J. Savage, Symmetric measures on Cartesian products, Trans. Amer. Math. Soc. 80 (1955), 470-501. Zbl0066.29604
  15. [15] R. L. Karandikar, A general principle for limit theorems in finitely additive probability, ibid. 273 (1982), 541-550. Zbl0507.60012
  16. [16] R. L. Karandikar, A general principle for limit theorems in finitely additive probability : the dependent case, J. Multivariate Anal. 24 (1988), 189-206. Zbl0638.60026
  17. [17] D. A. Lane and W. D. Sudderth, Diffuse models for sampling and predictive inference, Ann. Statist. 6 (1978), 1318-1336. Zbl0398.62003
  18. [18] R. A. Purves and W. D. Sudderth, Some finitely additive probability, Ann. Probab. 4 (1976), 259-276. Zbl0367.60034
  19. [19] R. A. Purves and W. D. Sudderth, Finitely additive zero-one laws, Sankhyā Ser. A 45 (1983), 32-37. Zbl0535.60030
  20. [20] S. Ramakrishnan, Finitely additive Markov chains, Ph.D. thesis, Indian Statistical Institute, 1980. Zbl0474.60027
  21. [21] S. Ramakrishnan, Finitely additive Markov chains, Trans. Amer. Math. Soc. 265 (1981), 247-272. Zbl0474.60027
  22. [22] S. Ramakrishnan, Central limit theorem in a finitely additive setting, Illinois J. Math. 28 (1984), 139-161. Zbl0514.60030
  23. [23] S. Ramakrishnan, Potential theory for finitely additive Markov chains, Stochastic Process. Appl. 16 (1984), 287-303. Zbl0538.60079
  24. [24] R. Ranga Rao, A note on finitely additive measures, Sankhyā Ser. A 18 (1958), 27-28. Zbl0082.26503
  25. [25] A. Sobczyk and P. C. Hammer, A decomposition of additive set functions, Duke Math. J. 11 (1944), 839-846. Zbl0063.07111
  26. [26] K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66. Zbl0046.05401

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.