Real Analysis for Graduate Students by Richard F. Bass
Real Analysis for Graduate Students - Table of Contents
- 1. Preliminaries
- 2. Families of sets
- 3. Measures
- 4. Construction of measures
- 5. Measurable functions
- 6. The Lebesgue integral
- 7. Limit theorems
- 8. Properties of Lebesgue integrals
- 9. Riemann integrals
- 10. Types of convergence
- 11. Product measures
- 12. Signed measures
- 13. The Radon-Nikodym theorem
- 14. Differentiation
- 15. Lp spaces
- 16. Fourier transforms
- 17. Riesz representation
- 18. Banach spaces
- 19. Hilbert spaces
- 20. Topology
- 21. Probability
- 22. Harmonic functions
- 23. Sobolev spaces
- 24. Singular integrals
- 25. Spectral theory
- 26. Distributions
- 27. Hints on exercises
What You Will Learn in Real Analysis for Graduate Students
Real Analysis for Graduate Students by Richard F. Bass is a rigorous, highly comprehensive graduate textbook designed to prepare PhD students in mathematics for qualifying examinations and advanced research. The text bridges foundational measure theory with modern advanced analysis, covering core topics across its exhaustive chapter index: Preliminaries, Measure Theory, and Outer Measures, Lebesgue Integration, Limit Theorems, and Product Measures, Signed Measures, Radon-Nikodym Theorem, and Differentiation, Lp Spaces, Fourier Transforms, and Riesz Representation, and advanced functional analysis topics including Banach and Hilbert Spaces, Distributions, Sobolev Spaces, and Spectral Theory.
This book serves as an invaluable guide for graduate students in pure and applied mathematics, statistics, and mathematical physics who need a solid foundation for partial differential equations, probability theory, and functional analysis. Bass combines concise theoretical expositions with carefully chosen exercises, ensuring readers develop strong analytical mastery.
Due to its broad scope and rigorous pedagogical design, it is widely recognized as an outstanding reference text for graduate real analysis and qualifying exam preparation. Rather than getting bogged down in excessive historical background, it equips advanced learners with the formal analytical tools necessary for modern mathematical research and advanced applied mathematics.
Book Details & Specifications
Title:
Real Analysis for Graduate Students by Richard F. Bass
Publisher:
CreateSpace
Year:
2011
Pages:
206
Type:
PDF
Language:
English
ISBN-10 #:
146639157X, 1481869140
ISBN-13 #:
9781466391574, 978-1481869140
License:
External Educational Resource
Amazon:
Amazon
About the Author: Richard Franklin Bass
The author Richard Franklin Bass
is a distinguished professor emeritus of mathematics at the University of Connecticut, renowned for his prolific research and textbook authorship in probability theory, stochastic processes, and real analysis.
Through Real Analysis for Graduate Students, Bass successfully synthesized a vast spectrum of advanced analytical tools into a clear, unified textbook. His precise mathematical style makes this text a masterpiece resource for graduate-level real and functional analysis.
Read or Downloadable Real Analysis for Graduate Students
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