Measure Theory Second Edition /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cohn, Donald L. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Birkhäuser, 2013.
Edición:2nd ed. 2013.
Colección:Birkhäuser Advanced Texts Basler Lehrbücher,
Temas:
Measure theory.
Mathematical analysis.
Probabilities.
Measure and Integration.
Analysis.
Probability Theory.
Acceso en línea:Texto Completo
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 µ^*-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.

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