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An open mapping theorem for Young measures
Author:
Hiroshi Tateishi
Journal:
Proc. Amer. Math. Soc. 136 (2008), 4027-4032
MSC (2000):
Primary 60B05, 54C60
Posted:
June 9, 2008
MathSciNet review:
2425744
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Abstract: Ditor and Eifler consider the open mapping theorem for the probability spaces. Here we attempt to generalize the theorem to the spaces of Young measures.
- 1.
Jean-Pierre
Aubin and Hélène
Frankowska, Set-valued analysis, Systems & Control:
Foundations & Applications, vol. 2, Birkhäuser Boston Inc.,
Boston, MA, 1990. MR 1048347
(91d:49001)
- 2.
Erik
J. Balder, Generalized equilibrium results for games with
incomplete information, Math. Oper. Res. 13 (1988),
no. 2, 265–276. MR 942618
(90d:90104), http://dx.doi.org/10.1287/moor.13.2.265
- 3.
C.
Castaing and M.
Valadier, Convex analysis and measurable multifunctions,
Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin, 1977. MR 0467310
(57 #7169)
- 4.
Seymour
Ditor Z. and Larry
Q. Eifler, Some open mapping theorems for
measures, Trans. Amer. Math. Soc. 164 (1972), 287–293. MR 0477729
(57 #17242), http://dx.doi.org/10.1090/S0002-9947-1972-0477729-X
- 5.
Larry
Q. Eifler, Open mapping theorems for probability measures on metric
spaces, Pacific J. Math. 66 (1976), no. 1,
89–97. MR
0453960 (56 #12212b)
- 6.
Paul
R. Milgrom and Robert
J. Weber, Distributional strategies for games with incomplete
information, Math. Oper. Res. 10 (1985), no. 4,
619–632. MR
812820 (86m:90186), http://dx.doi.org/10.1287/moor.10.4.619
- 7.
Andreas
Schief, An open mapping theorem for measures, Monatsh. Math.
108 (1989), no. 1, 59–70. MR 1018825
(91c:46040), http://dx.doi.org/10.1007/BF01300067
- 8.
J.
Warga, Optimal control of differential and functional
equations, Academic Press, New York, 1972. MR 0372708
(51 #8915)
- 9.
L.C. Young, Generalized curves and the existence of an attained absolute minimum, Calculus of Variations, C.R. Soc. Sc. Varsovie, 30(1937), 212-234.
- 1.
- J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990. MR 1048347 (91d:49001)
- 2.
- E. Balder, Generalized equilibrium results for games with incomplete information, Math. Oper. Res., 13(1988), 265-276. MR 942618 (90d:90104)
- 3.
- C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lect. Notes in Math., 580, Springer-Verlag, Berlin, 1977. MR 0467310 (57:7169)
- 4.
- S.Z. Ditor and L.Q. Eifler, Some open mapping theorems for measures, Trans. Amer. Math. Soc., 164(1972), 287-293. MR 0477729 (57:17242)
- 5.
- L.Q. Eifler, Open mapping theorems for probability measures on metric spaces, Pacific J. Math. 66(1976), 89-97. MR 0453960 (56:12212b)
- 6.
- P.R. Milgrom and R.J. Weber, Distributional strategies for games with incomplete information, Math. Oper. Res., 10(1985), 619-632. MR 812820 (86m:90186)
- 7.
- A. Schief, An open mapping theorem for measures, Monatsh. Math., 108(1989), 59-70. MR 1018825 (91c:46040)
- 8.
- J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972. MR 0372708 (51:8915)
- 9.
- L.C. Young, Generalized curves and the existence of an attained absolute minimum, Calculus of Variations, C.R. Soc. Sc. Varsovie, 30(1937), 212-234.
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Additional Information
Hiroshi Tateishi
Affiliation:
School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan
Email:
tateishi@soec.nagoya-u.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09375-1
PII:
S 0002-9939(08)09375-1
Keywords:
Young measure,
open mapping,
narrow topology
Received by editor(s):
December 29, 2006
Received by editor(s) in revised form:
September 7, 2007, and October 2, 2007
Posted:
June 9, 2008
Communicated by:
Richard C. Bradley
Article copyright:
© Copyright 2008 American Mathematical Society
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