Measure theory
Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter...
Guardado en:
| Autor principal: | |
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| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Colección: | Birkhäuser Advanced Texts Basler Lehrbücher
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| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme de l'éditeur (Springer) Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Measure Theory, Texte imprimé, 9781461469575 • Measure theory, Donald L. Cohn, 2nd edition, New York (N.Y.), Birkhäuser, Springer, 2013, 1 vol. (XXI-457 p.), Birkhäuser advanced texts, 978-1-4614-6955-1 • Measure theory, Donald L. Cohn, 2nd edition, New York (N.Y.), Birkhäuser, Springer, 2013, 1 vol. (XXI-457 p.), Birkhäuser advanced texts, 978-1-4614-6955-1 |
Tabla de Contenidos:
- 1. Measures
- Algebras and sigma-algebras
- Measures
- Outer measures
- Lebesgue measure
- Completeness and regularity
- Dynkin classes
- 2. Functions and Integrals
- Measurable functions
- Properties that hold almost everywhere
- The integral
- Limit theorems
- The Riemann integral
- Measurable functions again, complex-valued functions, and image measures
- 3. Convergence
- Modes of Convergence
- Normed spaces
- Definition of L^p and L^p
- Properties of L^p and L-p
- Dual spaces
- 4. Signed and Complex Measures
- Signed and complex measures
- Absolute continuity
- Singularity
- Functions of bounded variation
- The duals of the L^p spaces
- 5. Product Measures
- Constructions
- Fubini s theorem
- Applications
- 6. Differentiation
- Change of variable in R^d
- Differentiation of measures
- Differentiation of functions
- 7. Measures on Locally Compact Spaces
- Locally compact spaces
- The Riesz representation theorem
- Signed and complex measures; duality
- Additional properties of regular measures
- The ^*-measurable sets and the dual of L^1
- Products of locally compact spaces
- 8. Polish Spaces and Analytic Sets
- Polish spaces
- Analytic sets
- The separation theorem and its consequences
- The measurability of analytic sets
- Cross sections
- Standard, analytic, Lusin, and Souslin spaces
- 9. Haar Measure
- Topological groups
- The existence and uniqueness of Haar measure
- The algebras L^1 (G) and M (G)
- Appendices
- A. Notation and set theory
- B. Algebra
- C. Calculus and topology in R^d
- D. Topological spaces and metric spaces
- E. The Bochner integral
- F Liftings
- G The Banach-Tarski paradox
- H The Henstock-Kurzweil and McShane integralsBibliography
- Index of notation
- Index.