A version of Strassen's Theorem for vectorvalued measures
Authors:
A. Hirshberg and R. M. Shortt
Journal:
Proc. Amer. Math. Soc. 126 (1998), 16691671
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.
 1.
J.
Diestel and J.
J. Uhl Jr., Vector measures, American Mathematical Society,
Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical
Surveys, No. 15. MR 0453964
(56 #12216)
 2.
Richard
M. Dudley, Real analysis and probability, The Wadsworth &
Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books
& Software, Pacific Grove, CA, 1989. MR 982264
(91g:60001)
 3.
A. Hirshberg and R. M. Shortt, Strassen's Theorem for groupvalued charges, preprint.
 4.
John
L. Kelley and Isaac
Namioka, Linear topological spaces, SpringerVerlag, New York,
1976. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B.
J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott,
and Kennan T. Smith; Second corrected printing; Graduate Texts in
Mathematics, No. 36. MR 0394084
(52 #14890)
 5.
Michael
März and R.
M. Shortt, Weak convergence of vector measures, Publ. Math.
Debrecen 45 (1994), no. 12, 71–92. MR 1291803
(96g:28015)
 6.
Helmut
H. Schaefer, Banach lattices and positive operators,
SpringerVerlag, New York, 1974. Die Grundlehren der mathematischen
Wissenschaften, Band 215. MR 0423039
(54 #11023)
 7.
R.
M. Shortt, Strassen’s theorem for vector
measures, Proc. Amer. Math. Soc.
122 (1994), no. 3,
811–820. MR 1232144
(95a:28005), http://dx.doi.org/10.1090/S00029939199412321446
 8.
V.
Strassen, The existence of probability measures with given
marginals, Ann. Math. Statist. 36 (1965),
423–439. MR 0177430
(31 #1693)
 9.
B.
Z. Vulikh, Introduction to the theory of partially ordered
spaces, Translated from the Russian by Leo F. Boron, with the
editorial collaboration of Adriaan C. Zaanen and Kiyoshi Iséki,
WoltersNoordhoff Scientific Publications Ltd., Groningen, 1967. MR 0224522
(37 #121)
 10.
A.
C. Zaanen, Riesz spaces. II, NorthHolland Mathematical
Library, vol. 30, NorthHolland Publishing Co., Amsterdam, 1983. MR 704021
(86b:46001)
 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 groupvalued charges, preprint.
 4.
 J. L. Kelley, J. Namioka, et al., Linear Topological Spaces, Van Nostrand, Princeton, Reprinted by SpringerVerlag, New York, 1976. MR 52:14890
 5.
 M. März and R. M. Shortt, Weak convergence of vector measures, Publicationes Math. 45 (1994), 7192. MR 96g:28015
 6.
 H. H. Schaefer, Banach Lattices and Positive Operators, SpringerVerlag, Berlin, 1974. MR 54:11023
 7.
 R. M. Shortt, Strassen's Theorem for vector measures, Proc. Amer. Math. Soc. 122 (1994), 811820; 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), 423439. MR 31:1693
 9.
 B. C. Vulikh, Introduction to the Theory of Partially Ordered Spaces, WoltersNoordhoff, Groningen, 1967. MR 37:121
 10.
 A. C. Zaanen, Riesz Spaces II, NorthHolland, Amsterdam, 1983. MR 86b:46001
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Additional Information
A. Hirshberg
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 064590128
R. M. Shortt
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 064590128
DOI:
http://dx.doi.org/10.1090/S0002993998042361
PII:
S 00029939(98)042361
Received by editor(s):
July 24, 1996
Received by editor(s) in revised form:
October 28, 1996
Communicated by:
Clifford J. Earle, Jr.
Article copyright:
© Copyright 1998 American Mathematical Society
