More on Fatou's Lemma in Several Dimensions
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 334-339

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1987-047-0
Mots-clés : 28A20
Balder, Erik J. More on Fatou's Lemma in Several Dimensions. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 334-339. doi: 10.4153/CMB-1987-047-0
@article{10_4153_CMB_1987_047_0,
     author = {Balder, Erik J.},
     title = {More on {Fatou's} {Lemma} in {Several} {Dimensions}},
     journal = {Canadian mathematical bulletin},
     pages = {334--339},
     year = {1987},
     volume = {30},
     number = {3},
     doi = {10.4153/CMB-1987-047-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-047-0/}
}
TY  - JOUR
AU  - Balder, Erik J.
TI  - More on Fatou's Lemma in Several Dimensions
JO  - Canadian mathematical bulletin
PY  - 1987
SP  - 334
EP  - 339
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-047-0/
DO  - 10.4153/CMB-1987-047-0
ID  - 10_4153_CMB_1987_047_0
ER  - 
%0 Journal Article
%A Balder, Erik J.
%T More on Fatou's Lemma in Several Dimensions
%J Canadian mathematical bulletin
%D 1987
%P 334-339
%V 30
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-047-0/
%R 10.4153/CMB-1987-047-0
%F 10_4153_CMB_1987_047_0

[1] 1. Artstein, Z., A note on Fatou's lemma in several dimensions, J. Math. Econom. 6 (1979), pp. 277–282. Google Scholar

[2] 2. Ash, R.B., Real Analysis and Probability, Academic Press, 1972. Google Scholar

[3] 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] 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] 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] 6. Bhaskara Rao, K. P. S. and M. Bhaskara Rao, Theory of Charges, Academic Press, 1983. Google Scholar

[7] 7. Brooks, J.K. and Chacon, R.V., Continuity and compactness of measures, Adv. in Math. 37 (1980), pp. 16–26. Google Scholar

[8] 8. Cesari, L. and Suryanarayana, M.B., An existence theorem for Pareto problems, Nonlinear Anal. 2 (1978), pp. 225–233. Google Scholar

[9] 9. Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton University Press, Princeton, 1974. Google Scholar

[10] 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] 11. Plachky, D., StochastikAnwendungen und Ubungen, Akademische Verlagsgesellschaft , Wiesbaden, 1983. Google Scholar

[12] 12. Schmeidler, D., Fatou's lemma in several dimensions, Proc. Amer. Math. Soc. 24 (1970), pp. 300–306. Google Scholar

Cité par Sources :