19. Measurable set-valued maps. Measurable selections and measurable choice theorems

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Contents VII
4. Part I: Convex analysis
5. 1. Convex sets and their properties 3
6. 2. The convex hull of a set. The interior of convex sets 7
7. 3. The affine hull of sets. The relative interior of convex sets 13
8. 4. Separation theorems for convex sets 21
9. 5. Convex functions 29
10. 6. Closedness, boundedness, continuity, and Lipschitz property of convex functions 37
11. 7. Conjugate functions 45
12. 8. Support functions 51
13. 9. Differentiability of convex functions and the subdifferential 59
14. 10. Convex cones 69
15. 11. A little more about convex cones in infinite-dimensional spaces 75
16. 12. A problem of linear programming 79
17. 13. More about convex sets and convex hulls 83
18. Part II: Set-valued analysis
19. 14. Introduction to the theory of topological and metric spaces 91
20. 15. The Hausdorff metric and the distance between sets 95
21. 16. Some fine properties of the Hausdorff metric 103
22. 17. Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps 109
23. 18. A base of topology of the space H_c(X) 121
24. 19. Measurable set-valued maps. Measurable selections and measurable choice theorems 123
25. 20. The superposition set-valued operator 129
26. 21. The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations 135
27. 22. Special selections of set-valued maps 141
28. 23. Differential inclusions 149
29. 24. Fixed points and coincidences of maps in metric spaces 155
30. 25. Stability of coincidence points and properties of covering maps 165
31. 26. Topological degree and fixed points of set-valued maps in Banach spaces 171
32. 27. Existence results for differential inclusions via the fixed point method 187
33. Notation 191
34. Bibliography 195
35. Index 199