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More on Fatou's Lemma in Several Dimensions

Published online by Cambridge University Press:  20 November 2018

Erik J. Balder
Erik J. Balder*
Affiliation:
Mathematical Institute University of Utrecht Utrecht, Netherlands
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Abstract

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Recently, Balder proved a version of FatoiTs lemma in several dimensions which, inter alia, generalizes a version of this lemma due to Artstein. Here we show how the latter result can be used to derive the former, by using Chacon's biting lemma.

Keywords

28A20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 334 - 339
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Artstein, Z., A note on Fatou's lemma in several dimensions, J. Math. Econom. 6 (1979), pp. 277–282.Google Scholar
2. Ash, R.B., Real Analysis and Probability, Academic Press, 1972.Google Scholar
3. Balder, E.J., A unifying note on Fatou's lemma in several dimensions, Math. Oper. Res. 9 (1984), pp. 267–275.Google Scholar
4. Balder, E.J., A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control Optim. 22 (1984), pp. 570–599.Google Scholar
5. Balder, E.J., Existence results without convexity conditions for general problems of optimal control with singular components, J. Math. Anal. Appl. 101 (1984), pp. 527—539.Google Scholar
6. Bhaskara Rao, K. P. S. and M. Bhaskara Rao, Theory of Charges, Academic Press, 1983.Google Scholar
7. Brooks, J.K. and Chacon, R.V., Continuity and compactness of measures, Adv. in Math. 37 (1980), pp. 16–26.Google Scholar
8. Cesari, L. and Suryanarayana, M.B., An existence theorem for Pareto problems, Nonlinear Anal. 2 (1978), pp. 225–233.Google Scholar
9. Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton University Press, Princeton, 1974.Google Scholar
10. Hildenbrand, W. and Mertens, J.F., On Fatou's lemma in several dimensions, Z. Wahrsch. Th. Verw. Geb. 17(1971), pp. 151–155.Google Scholar
11. Plachky, D., Stochastik—Anwendungen und Ubungen, Akademische Verlagsgesellschaft , Wiesbaden, 1983.Google Scholar
12. Schmeidler, D., Fatou's lemma in several dimensions, Proc. Amer. Math. Soc. 24 (1970), pp. 300–306.Google Scholar