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Problems in Real and Functional Analysis

Alberto Torchinsky Indiana University, Bloomington, IN
Available Formats:
Hardcover ISBN: 978-1-4704-2057-4
Product Code: GSM/166
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $67.20 Electronic ISBN: 978-1-4704-2781-8 Product Code: GSM/166.E List Price:$79.00
MAA Member Price: $71.10 AMS Member Price:$63.20
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List Price: $126.00 MAA Member Price:$113.40
AMS Member Price: $100.80 Click above image for expanded view Problems in Real and Functional Analysis Alberto Torchinsky Indiana University, Bloomington, IN Available Formats:  Hardcover ISBN: 978-1-4704-2057-4 Product Code: GSM/166  List Price:$84.00 MAA Member Price: $75.60 AMS Member Price:$67.20
 Electronic ISBN: 978-1-4704-2781-8 Product Code: GSM/166.E
 List Price: $79.00 MAA Member Price:$71.10 AMS Member Price: $63.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$126.00 MAA Member Price: $113.40 AMS Member Price:$100.80
• Book Details

Volume: 1662015; 467 pp
MSC: Primary 26; 28; 46; 47;

It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems.

The Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most “natural” rather than the most elegant solution is presented.

Graduate students and researchers interested in learning and teaching real and functional analysis at the graduate level.

• Part 1. Problems
• Chapter 1. Set theory and metric spaces
• Chapter 2. Measures
• Chapter 3. Lebesgue measure
• Chapter 4. Measurable and integrable functions
• Chapter 5. $L^p$ spaces
• Chapter 6. Sequences of functions
• Chapter 7. Product measures
• Chapter 8. Normed linear spaces. Functionals
• Chapter 9. Normed linear spaces. Linear operators
• Chapter 10. Hilbert spaces
• Part 2. Solutions
• Chapter 11. Set theory and metric spaces
• Chapter 12. Measures
• Chapter 13. Lebesgue measure
• Chapter 14. Measurable and integrable functions
• Chapter 15. $L^p$ spaces
• Chapter 16. Sequences of functions
• Chapter 17. Product measures
• Chapter 18. Normed linear spaces. Functionals
• Chapter 19. Normed linear spaces. Linear operators
• Chapter 20. Hilbert spaces

• Reviews

• The book is written in a very clear style and is very useful for graduate students to extend their vision of real and functional analysis.

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1662015; 467 pp
MSC: Primary 26; 28; 46; 47;

It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems.

The Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most “natural” rather than the most elegant solution is presented.

Graduate students and researchers interested in learning and teaching real and functional analysis at the graduate level.

• Part 1. Problems
• Chapter 1. Set theory and metric spaces
• Chapter 2. Measures
• Chapter 3. Lebesgue measure
• Chapter 4. Measurable and integrable functions
• Chapter 5. $L^p$ spaces
• Chapter 6. Sequences of functions
• Chapter 7. Product measures
• Chapter 8. Normed linear spaces. Functionals
• Chapter 9. Normed linear spaces. Linear operators
• Chapter 10. Hilbert spaces
• Part 2. Solutions
• Chapter 11. Set theory and metric spaces
• Chapter 12. Measures
• Chapter 13. Lebesgue measure
• Chapter 14. Measurable and integrable functions
• Chapter 15. $L^p$ spaces
• Chapter 16. Sequences of functions
• Chapter 17. Product measures
• Chapter 18. Normed linear spaces. Functionals
• Chapter 19. Normed linear spaces. Linear operators
• Chapter 20. Hilbert spaces
• The book is written in a very clear style and is very useful for graduate students to extend their vision of real and functional analysis.