References
Z. Artstein, A Note on Fatou's Lemma in Several Dimensions. J. Math. Econom.6, 277–282 (1979).
R. J. Aumann, Integrals of Set-Valued Functions. J. Math. Anal. Appl.12, 1–12 (1965).
C.Castaing and M.Valadier, Convex Analysis and Measurable Multifunctions. In: LNM580, Berlin-Heidelberg-New York 1977.
R. Datko, On the Integration of Set-valued Mappings in a Banach Space. Fund. Math.78, 205–208 (1973).
J. Diestel andJ. Uhl, Vector Measures. In: Mathematical Surveys15, Amer. Math. Soc., Providence, RI 1977.
L. Dsosu andC. Shaozhong, On Fixed Point Theorems for Random Set-Valued Maps. Nonlinear Anal.7, 309–323 (1983).
E.Hewitt and K.Stromberg, Real and Abstract Analysis. Berlin-Heidelberg-New York 1965.
W. Hildenbrand andJ. Mertens, On Fatou's Lemma in Several Dimensions. Z. für Wahrsch. Verw. Gebiete17, 151–155 (1971).
M. Ali Khan, On the Integration of Set-Valued Mappings in a Non-Reflexive Banach Space, II. Simon Stevin59, 257–267 (1985).
M. Ali Khan andM. Majumdar, Weak Sequential Compactness inL 1 (μ, X) and an Approximate Version of Fatou's Lemma. J. Math. Anal. Appl.114, 569–573 (1986).
D. Schmeidler, Fatou's Lemma in Several Dimensions. Proc. Amer. Math. Soc.24, 300–306 (1970).
N. C. Yannelis, Equilibria in Non-Cooperative Models of Competition. J. Econom. Theory41, 96–111 (1987).
N. C.Yannelis, Fatou's Lemma in Infinite Dimensional Spaces. Proc. Amer. Math. Soc. 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rustichini, A. A counterexample and an exact version of Fatou's lemma in infinite dimensional spaces. Arch. Math 52, 357–362 (1989). https://doi.org/10.1007/BF01194410
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01194410