Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T21:23:05.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Komlos Limits and Fatou's Lemma in Several Dimensions

Published online by Cambridge University Press:  20 November 2018

Frank H. Page Jr.
Frank H. Page Jr.*
Affiliation:
Department of Finance University of Alabama Tuscaloosa, Alabama 35487 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using Komlos' Theorem, a sequence decomposition result due to Gaposhkin, and two results due to Artstein, we prove a result concerning the properties of Komlos limits. We then show that a stronger version of Fatou's Lemma in several dimensions can be deduced from Artstein's version of the Lemma. The version of Fatou's Lemma proved here subsumes the most recent version of the Lemma in several dimensions given by Balder.

Keywords

28B0528A2046G10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 109 - 112
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Artstein, Z., A Note on Fatou's Lemma in Several Dimensions, J. Math. Econom. 6 (1979), 277–282.Google Scholar
2. Balder, E. J., A Unifying Note on Fatou 's Lemma in Several Dimensions, Math. Oper. Res. 9( 1984), 267-275. 3 , More on Fatou's Lemma in Several Dimensions, Canad. Math. Bull. 30 (1987), 334–339.Google Scholar
4. Gaposhkin, V. F., Convergence and Limit Theorems for Sequences of Random Variables, Theor. Probability Appl. 17 (1972), 379–400.Google Scholar
5. Hildenbrand, W., Core and Equilibria of a Large Economy. Princeton University Press, Princeton, 1974.Google Scholar
6. Hildenbrand, W. and Mertens, J. F., On Fatou's Lemma in Several Dimensions, Z. Wahrsch. Th. Verw. Geb. 17 (1971), 151–155.Google Scholar
7. Komlos, J., A Generalization of a Problem ofSteinhaus, Acta Math. Acad. Sci. Hungar. 18( 1967), 217–229.Google Scholar
8. Schmeidler, D., Fatou's Lemma in Several Dimensions, Proc. Amer. Math. Soc. 24 (1970), 300–306.Google Scholar