Essentials of Measure Theory

• Main Author: Kubrusly, Carlos S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Edition: 1st ed. 2015.
• Subjects: Mathematics.; Measure theory.; Topology.; Measure and Integration.

Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgu...

Table of Contents:

• Preface
• Part I. Introduction to Measure and Integration.-1. Measurable Functions
• 2. Measure on a σ-Algebra
• 3. Integral of Nonnegative Functions
• 4. Integral of Real-Valued Functions
• 5. Banach Spaces Lp
• 6. Convergence of Functions
• 7. Decomposition of Measures
• 8. Extension of Measures
• 9. Product Measures
• Part II
• 10. Remarks on Integrals
• 11. Borel Measure
• 12. Representation Theorems
• 13. Invariant Measures
• References
• Index.