Connections between recent Olech-type lemmas and Visintin's theorem
Balder, Erik
Banach Center Publications, Tome 31 (1995), p. 47-52 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

A recent Olech-type lemma of Artstein-Rzeżuchowski [2] and its generalization in [7] are shown to follow from Visintin's theorem, by exploiting a well-known property of extreme points of the integral of a multifunction.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262876 
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p47bwm,
     author = {Balder, Erik},
     title = {Connections between recent Olech-type lemmas and Visintin's theorem},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {47-52},
     zbl = {0838.28010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p47bwm}
}

Balder, Erik. Connections between recent Olech-type lemmas and Visintin's theorem. Banach Center Publications, Tome 31 (1995) pp. 47-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p47bwm/

[000] [1] Z. Artstein, A note on Fatou's lemma in several dimensions, J. Math. Econom. 6 (1979), 277-282. | Zbl 0433.28004

[001] [2] Z. Artstein and T. Rzeżuchowski, A note on Olech's lemma, Studia Math. 98 (1991), 91-94.

[002] [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.

[003] [4] R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. | Zbl 0163.06301

[004] [5] E. J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control Optim. 22 (1984), 570-599. | Zbl 0549.49005

[005] [6] E. J. Balder, On weak convergence implying strong convergence in L1-spaces, Bull Austral. Math. Soc. 33 (1986), 363-368. | Zbl 0579.46018

[006] [7] E. J. Balder, A unified approach to several results involving integrals of multifunctions, Set-Valued Anal. 2 (1994), 63-75. | Zbl 0803.28008

[007] [8] E. J. Balder, On equivalence of strong and weak convergence in L1-spaces under extreme point conditions, Israel J. Math. 75 (1991), 21-47. | Zbl 0758.28005

[008] [9] J. K. Brooks and R. V. Chacon, Continuity and compactness of measures, Adv. in Math. 37 (1980), 16-26. | Zbl 0463.28003

[009] [10] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977. | Zbl 0346.46038

[010] [11] V. F. Gaposhkin, Convergence and limit theorems for sequences of random variables, Theory Probab. Appl. 17 (3) (1972), 379-400.

[011] [12] J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1964. | Zbl 0137.11203

[012] [13] J. Neveu, Extremal solutions of a control system, J. Differential Equations 2 (1966), 74-101.

[013] [14] J. Neveu, Existence theory in optimal control, in: Control Theory and Topics in Functional Analysis, IAEA, Vienna, 1976, 291-328.

[014] [15] J. Pfanzagl, Convexity and conditional expectations, Ann. Probab. 2 (1974), 490-494. | Zbl 0285.60002

[015] [16] M. Slaby, Strong convergence of vector-valued pramarts and subpramarts, Probab. Math. Statist. 5 (1985), 187-196. | Zbl 0626.60039

[016] [17] M. Valadier, Young measures, weak and strong convergence and the Visintin-Balder theorem, Set-Valued Anal. 2 (1994), 357-367. | Zbl 0818.46031

[017] [18] A. Visintin, Strong convergence results related to strict convexity, Comm. Partial Differential Equations 9 (1984), 439-466. | Zbl 0545.49019