Introduction to Real Analysis

• Main Author: Heil, Christopher (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Graduate Texts in Mathematics, 280
• Subjects: Measure theory.; Operator theory.; Topology.; Functional analysis.; Fourier analysis.; Measure and Integration.; Operator Theory.; Functional Analysis.; Fourier Analysis.

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author's lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue...

Table of Contents:

• Preliminaries
• 1. Metric and Normed Spaces
• 2. Lebesgue Measure
• 3. Measurable Functions
• 4. The Lebesgue Integral
• 5. Differentiation
• 6. Absolute Continuity and the Fundamental Theorem of Calculus
• 7. The L<i>p Spaces
• 8. Hilbert Spaces and L^2(E)
• 9. Convolution and the Fourier Transform.