UID:
almahu_9947367584802882
Umfang:
1 online resource (191 p.)
ISBN:
1-281-98416-7
,
9786611984168
,
0-08-087131-3
Serie:
North-Holland mathematics studies ; 20
Inhalt:
Vector measures and control systems
Anmerkung:
Includes indexes.
,
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
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3. Completeness4. 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
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6. Non-Atomic Vector Measures7. 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
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CHAPTER IX. CONTROL SYSTEMS1. 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
,
English
Weitere Ausg.:
ISBN 0-444-11040-2
Sprache:
Englisch
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