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A version of Strassen's Theorem for vector-valued measures
Author(s):
A.
Hirshberg;
R.
M.
Shortt
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1669-1671.
MSC (1991):
Primary 28B05;
Secondary 30C62, 46B42
MathSciNet review:
1443832
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Abstract:
A formulation of Strassen's Theorem is given for measures taking values in a Banach lattice. The main result (Theorem 2) corrects earlier work of the second author.
References:
- 1.
- J. Diestel and J. J. Uhl, Jr., Vector Measures, Mathematical Surveys, No. 15, Amer. Math. Soc., Providence, RI, 1977. MR 56:12216
- 2.
- R. M. Dudley, Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, 1989. MR 91g:60001
- 3.
- A. Hirshberg and R. M. Shortt, Strassen's Theorem for group-valued charges, pre-print.
- 4.
- J. L. Kelley, J. Namioka, et al., Linear Topological Spaces, Van Nostrand, Princeton, Reprinted by Springer-Verlag, New York, 1976. MR 52:14890
- 5.
- M. März and R. M. Shortt, Weak convergence of vector measures, Publicationes Math. 45 (1994), 71-92. MR 96g:28015
- 6.
- H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, Berlin, 1974. MR 54:11023
- 7.
- R. M. Shortt, Strassen's Theorem for vector measures, Proc. Amer. Math. Soc. 122 (1994), 811-820; Correction, Proc. Amer. Math. Soc., this number. MR 95a:28005
- 8.
- V. Strassen, The existence of probability measures with given marginals, Ann. Math. Stat. 36 (1965), 423-439. MR 31:1693
- 9.
- B. C. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen, 1967. MR 37:121
- 10.
- A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983. MR 86b:46001
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Additional Information:
A.
Hirshberg
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459-0128
R.
M.
Shortt
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459-0128
DOI:
10.1090/S0002-9939-98-04236-1
PII:
S 0002-9939(98)04236-1
Received by editor(s):
July 24, 1996
Received by editor(s) in revised form:
October 28, 1996
Communicated by:
Clifford J. Earle, Jr.
Copyright of article:
Copyright
1998,
American Mathematical Society
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