Measure Theory Second Edition /

• Κύριος συγγραφέας: Cohn, Donald L. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Birkhäuser, 2013.
• Έκδοση: 2nd ed. 2013.
• Σειρά: Birkhäuser Advanced Texts Basler Lehrbücher,
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Probabilities.; Measure and Integration.; Analysis.; Probability Theory and Stochastic Processes.

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...

Πίνακας περιεχομένων:

• 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.