Vector Measures and Control Systems
Elsevier (Publisher)
Published on 21. September 2011
179 pages
978-0-08-087131-8 (ISBN)
Description
Vector Measures and Control Systems
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Content
- Front Cover
- Vector Measures and Control Systems
- Copyright Page
- Table of Contents
- CHAPTER I. PRELIMINARIES
- 1. Locally Convex Cpaces
- 2. Extreme and Exposed Points
- 3. Measure Spaces
- 4. Conical Measures
- Remarks
- CHAPTER II. VECTOR MEASURES AND INTEGRATION
- 1. Vector Measures
- Variation and Semi-Variation
- 2. Integration
- 3. Integrability of Bounded Functions
- 4. Limit Theorems
- 5. A Sufficient Condition for Integrability
- 6. An Isomorphism Theorem
- 7. Direct Sum of Vector Measures
- Remarks
- CHAPTER III. FUNCTION SPACES I
- 1. Topologies
- 2. Some Relations Between Topologies
- 3. Completeness
- 4. Lattice Completeness
- 5. Weak Compactness
- 6. Completion
- 7. Extreme and Exposed Points
- 8. Vector-Valued Functions
- Remarks
- CHAPTER IV. CLOSED VECTOR MEASURES
- 1. Properties of the Integration Mapping
- 2. Closed Vector Measures
- 3. Closure of a Vector Measure
- 4. Completeness of L1 (m)
- 5. Lattice Completeness
- 6. Weak Compactness of the Range
- 7. Sufficient Conditions for Closedness
- Remarks
- CHAPTER V. LIAPUNOV VECTOR MEASURES
- 1. Liapunov Vector Measures
- 2. Consequences of the Test
- 3. Liapunov Decomposition
- 4. Moment Sequences
- 5. Liapunov Extension
- 6. Non-Atomic Vector Measures
- 7. Examples of Bang-Bang Control
- Remarks
- CHAPTER VI. EXTREME AND EXPOSED POINTS OF THE RANGE
- 1 . Extreme Points
- 2. Properties of the Set of Extreme Points
- 3 . Rybakov's Theorem
- 4. Exposed Points of the Range
- Remarks
- CHAPTER VII. THE RANGE OF A VECTOR MEASURE
- 1. The Problem
- 2. The Conical Measure Associated with a Vector Measure
- 3. The Relation Between m and ?(m)
- 4. Consequences of the Test
- Remarks
- CHAPTER VIII. FUNCTION SPACES II
- 1. Set-Valued Functions
- 2. Measurable Selections
- 3 . Sequences of Measures
- 4. Extreme Points
- Remarks
- CHAPTER IX. CONTROL SYSTEMS
- 1. Attainable Set
- 2. Extreme Points of the Attainable Set
- 3. Liapunov Control Systems
- 4. Non-Atomic Control Systems
- 5. Time-optimal Control
- Remarks
- BIBLIOGRAPHY
- NOTATION INDEX
- INDEX
