Introduction . . . . . . . . 1
Chapter O. Background Notes . 9
Introduction . . . . . . . . 9
1. Continuous Partitions of Unity. 9
2. Absolutely Continuous Functions 12
3. Some Compactness Theorems . . 13
4. Weak Convergence and Asymptotic Center of Bounded Sequences 15
5. Closed Convex Hulls and the Mean-Value Theorem . . . . .. 18
6. Lower Semicontinuous Convex Functions and Projections of Best
Approximation. . . . . . . . . . . . . 21
7. A Concise Introduction to Convex Analysis 29
Chapter 1. Set-Valued Maps . . . . . . . .
Introduction . . . . . . . . . . . . . . .
1. Set-Valued Maps and Continuity Concepts
2. Examples of Set-Valued Maps. . . . . .
3. Continuity Properties of Maps with Closed Convex Graph
4. Upper Hemicontinuous Maps and the Convergence Theorem
5. Hausdorff Topology .
6. The Selection Problem
7. The Minimal Selection
8. Chebishev Selection .
9. The Barycentric Selection.
10. Selection Theorems for Locally Selectionable Maps
11. Michael's Selection Theorem . . . . . . . . . .
12. The Approximate Selection Theorem and Kakutani's Fixed
Theorem ..... .
13. O'-Selectionable Maps.
14. Measurable Selections
Chapter 2. Existence of Solutions to Differential Inclusions
Introduction . . . . . . . . . . . . .
1. Convex Valued Differential Inclusions. . . . . . . .
Chapter 3. Differential Inclusions with Maximal Monotone Maps
Chapter 4. Viability Theory: The Nonconvex Case
Chapter S. Viability Theory and Regulation of Controled Systems: The
Convex Case
Chapter 6. Liapunov Functions