Integral and Functional Analysis (Updated Edition)


Jie Xiao, PhD (Author) – University Research Professor, Memorial University of Newfoundland, Canada

Series: Mathematics Research Developments

BISAC: MAT034000

Target Audience: Senior undergraduate students and graduate students

This textbook is based on three closely related courses: 1) Integration and Metric Spaces; 2) Lebesgue Integration; 3) Functional Analysis. Although the contents have been used for joint undergraduate and graduate courses, this textbook is designed primarily for senior undergraduate students. The prerequisites of this textbook are deliberately modest, and it is assumed that the students have some familiarity with calculus and linear algebra plus the basic (direct, indirect) proof methods.




Chapter 1. Preliminaries

Chapter 2. Riemann Integral

Chapter 3.Riemann-Stieltjes Integrals

Chapter 4. Lebesgue-Radon-Stieltjes Integrals

Chapter 5. Absolute Continuities in Lebesgue Integrals

Chapter 6. Metric Spaces

Chapter 7. Continuous Mappings

Chapter 8. Normed Linear Spaces

Chapter 9. Banach Spaces via Operators and Functionals

Chapter 10. Hilbert Spaces and Their Operators


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