|
A type of Strassen's theorem for positive vector measures with values in dual spaces
Author(s):
Jun
Kawabe
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3291-3300.
MSC (2000):
Primary 28B05, 28A33;
Secondary 46A40
Posted:
April 28, 2000
MathSciNet review:
1670387
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
- 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
28B05, 28A33,
46A40
Retrieve articles in all Journals with
MSC (2000):
28B05, 28A33,
46A40
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:
10.1090/S0002-9939-00-05384-3
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
|
