7. Tree Measures

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• 作者：Charles Favre ; Mattias Jonsson
• 刊名：Lecture Notes in Mathematics
• 出版年：2004
• 出版时间：2004
• 年：2004
• 卷：1853
• 期：1
• 页码：pp.151-192
• 全文大小：498 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Dynamical Systems and Ergodic Theory
  Mathematical Biology
  Partial Differential Equations
  Functional Analysis
  Abstract Harmonic Analysis
  Group Theory and Generalizations
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1617-9692

文摘

7.1. Outline 7.1.1. The Unbranched Case 7.1.2. The General Case 7.1.3. Organization 7.2. More on the Weak Topology 7.2.1. Definition 7.2.2. Basic properties 7.2.3. Subtrees 7.2.4. Connectedness 7.2.5. Compactness 7.3. Borel Measures 7.3.1. Basic Properties 7.3.2. Radon Measures 7.3.3. Spaces of Measures 7.3.4. The Support of a Measure 7.3.5. A Generating Algebra 7.3.6. Every Complex Borel Measure is Radon 7.4. Functions of Bounded Variation 7.4.1. Definitions 7.4.2. Decomposition 7.4.3. Limits and Continuity 7.4.4. The Space N\mathcal {N} 7.4.5. Finite Trees 7.4.6. Proofs 7.5. Representation Theorem I 7.5.1. First Step 7.5.2. Second Step: from Functions to Measures 7.5.3. Total Variation 7.6. Complex Tree Potentials 7.6.1. Definition 7.6.2. Directional Derivatives 7.7. Representation Theorem II 7.8. Atomic Measures 7.9. Positive Tree Potentials 7.9.1. Definition 7.9.2. Jordan Decompositions 7.10. Weak Topologies and Compactness 7.11. Restrictions to Subtrees 7.12. Inner Products 7.12.1. Hausdorff Measure 7.12.2. The Positive Case 7.12.3. Properties 7.12.4. The Complex Case 7.12.5. Topologies and Completeness