Connections between recent Olech-type lemmas and Visintin's theorem

Erik Balder

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 47-52
  • ISSN: 0137-6934

Abstract

top
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.

How to cite

top

Balder, Erik. "Connections between recent Olech-type lemmas and Visintin's theorem." Banach Center Publications 32.1 (1995): 47-52. <http://eudml.org/doc/262876>.

@article{Balder1995,
abstract = {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.},
author = {Balder, Erik},
journal = {Banach Center Publications},
keywords = {integrals of multifunctions; measurable selections; extreme point; strong convergence; weak convergence},
language = {eng},
number = {1},
pages = {47-52},
title = {Connections between recent Olech-type lemmas and Visintin's theorem},
url = {http://eudml.org/doc/262876},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Balder, Erik
TI - Connections between recent Olech-type lemmas and Visintin's theorem
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 47
EP - 52
AB - 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.
LA - eng
KW - integrals of multifunctions; measurable selections; extreme point; strong convergence; weak convergence
UR - http://eudml.org/doc/262876
ER -

References

top
  1. [1] Z. Artstein, A note on Fatou's lemma in several dimensions, J. Math. Econom. 6 (1979), 277-282. Zbl0433.28004
  2. [2] Z. Artstein and T. Rzeżuchowski, A note on Olech's lemma, Studia Math. 98 (1991), 91-94. 
  3. [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990. 
  4. [4] R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. Zbl0163.06301
  5. [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. Zbl0549.49005
  6. [6] E. J. Balder, On weak convergence implying strong convergence in L 1 -spaces, Bull Austral. Math. Soc. 33 (1986), 363-368. Zbl0579.46018
  7. [7] E. J. Balder, A unified approach to several results involving integrals of multifunctions, Set-Valued Anal. 2 (1994), 63-75. Zbl0803.28008
  8. [8] E. J. Balder, On equivalence of strong and weak convergence in L 1 -spaces under extreme point conditions, Israel J. Math. 75 (1991), 21-47. Zbl0758.28005
  9. [9] J. K. Brooks and R. V. Chacon, Continuity and compactness of measures, Adv. in Math. 37 (1980), 16-26. Zbl0463.28003
  10. [10] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977. Zbl0346.46038
  11. [11] V. F. Gaposhkin, Convergence and limit theorems for sequences of random variables, Theory Probab. Appl. 17 (3) (1972), 379-400. 
  12. [12] J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1964. Zbl0137.11203
  13. [13] J. Neveu, Extremal solutions of a control system, J. Differential Equations 2 (1966), 74-101. 
  14. [14] J. Neveu, Existence theory in optimal control, in: Control Theory and Topics in Functional Analysis, IAEA, Vienna, 1976, 291-328. 
  15. [15] J. Pfanzagl, Convexity and conditional expectations, Ann. Probab. 2 (1974), 490-494. Zbl0285.60002
  16. [16] M. Slaby, Strong convergence of vector-valued pramarts and subpramarts, Probab. Math. Statist. 5 (1985), 187-196. Zbl0626.60039
  17. [17] M. Valadier, Young measures, weak and strong convergence and the Visintin-Balder theorem, Set-Valued Anal. 2 (1994), 357-367. Zbl0818.46031
  18. [18] A. Visintin, Strong convergence results related to strict convexity, Comm. Partial Differential Equations 9 (1984), 439-466. Zbl0545.49019

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.