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A type of Strassen's theorem for positive vector measures with values in dual spaces


Author: Jun Kawabe
Journal: Proc. Amer. Math. Soc. 128 (2000), 3291-3300
MSC (2000): Primary 28B05, 28A33; Secondary 46A40
DOI: https://doi.org/10.1090/S0002-9939-00-05384-3
Published electronically: April 28, 2000
MathSciNet review: 1670387
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Abstract:

In this paper, we extend a type of Strassen's theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.


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  • 1. M. Dekiert, Kompaktheit, Fortsetzbarkeit und Konvergenz von Vectormaßen, Dissertation, University of Essen, 1991.
  • 2. J. Diestel and J. J. Uhl, Vector Measures, Amer. Math. Soc. Surveys Vol. 15, Amer. Math. Soc., Providence RI, 1977. MR 56:12216
  • 3. R. M. Dudley, Real Analysis and Probability, Wadsworth and Brooks/Cole, Pacific Grove, 1989. MR 91g:60001
  • 4. N. Dunford and J. T. Schwartz, Linear Operators, Part 1: General Theory, John Wiley & Sons, New York, 1988. MR 90g:47001a
  • 5. D. A. Edwards, On the existence of probability measures with given marginals, Ann. Inst. Fourier $($Grenoble$)$ 28 (1978), 53-78. MR 81i:28009
  • 6. J. Hoffmann-Jørgensen, Probability in Banach Spaces, Ecole d'Été de Probabilités de Saint-Flour VI-1976, Lecture Notes in Math. 598 (1977), 1-186. MR 57:1595
  • 7. A. Hirshberg and R. M. Shortt, A version of Strassen's theorem for vector-valued measures, Proc. Amer. Math. Soc. 126 (1998), 1669-1671. MR 98i:28014
  • 8. H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981. MR 83h:46008
  • 9. J. L. Kelley and I. Namioka, Linear Topological Spaces, Van Nostrand, New York, 1963. MR 29:3851
  • 10. I. Kluvánek and G. Knowles, Vector Measures and Control Systems, North-Holland, 1976. MR 58:17033
  • 11. L. LeCam, Convergence in distribution of stochastic processes, Univ. California Publ. Statist. 2 (1957), 207-236. MR 19:128a
  • 12. D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165. MR 41:3706
  • 13. M. März and R. M. Shortt, Weak convergence of vector measures, Publ. Math. Debrecen 45 (1994), 71-92. MR 96g:28015
  • 14. C. W. McArthur, On a theorem of Orlicz and Pettis, Pacific J. Math. 22 (1967), 297-302. MR 35:4702
  • 15. Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1 (1956), 177-238. MR 18:943b
  • 16. H. H. Schaefer, Topological Vector Spaces, Springer-Verlag, New York, 1971. MR 49:7722
  • 17. R. Schatten, Norm Ideals of Completely Continuous Operators, Springer-Verlag, New York, 1970. MR 41:2449
  • 18. R. M. Shortt, Strassen's marginal problem in two or more dimensions, Z. Wahrsch. Verw. Gebiete. 64 (1983), 313-325. MR 84i:60023
  • 19. H. J. Skala, The existence of probability measures with given marginals, Ann. Probab. 21 (1993), 136-142. MR 94f:60004
  • 20. O. G. Smolyanov and S. V. Fomin, Measures on topological linear spaces, Russian Math. Surveys 31 (1976), 3-56. MR 54:8776
  • 21. V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist. 36 (1965), 423-439. MR 31:1693
  • 22. F. Topsøe, Topology and Measure, Lecture Notes in Math. 133, Springer-Verlag, New York, 1970. MR 54:10546
  • 23. F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967. MR 37:726
  • 24. V. S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. Ser. II 48 (1965), 161-228. MR 26:6342

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Additional Information

Jun Kawabe
Affiliation: Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
Email: jkawabe@gipwc.shinshu-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-00-05384-3
Keywords: Strassen's theorem, positive vector measure, weak convergence of vector measures, barreled locally convex space, Riesz space
Received by editor(s): July 9, 1998
Received by editor(s) in revised form: December 20, 1998
Published electronically: April 28, 2000
Additional Notes: This research was supported by Grant-in-Aid for General Scientific Research No. 11640160, the Ministry of Education, Science, Sports and Culture, Japan.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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