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The Lebesgue Integral for Undergraduates
 
The Lebesgue Integral for Undergraduates
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-93951-207-9
Product Code:  TEXT/27
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-61444-620-0
Product Code:  TEXT/27.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-93951-207-9
eBook: ISBN:  978-1-61444-620-0
Product Code:  TEXT/27.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
The Lebesgue Integral for Undergraduates
Click above image for expanded view
The Lebesgue Integral for Undergraduates
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-93951-207-9
Product Code:  TEXT/27
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-61444-620-0
Product Code:  TEXT/27.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-93951-207-9
eBook ISBN:  978-1-61444-620-0
Product Code:  TEXT/27.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 272015; 284 pp

    This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text's use of a method labeled the “Daniell-Riesz approach.” The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist.

    Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions.

    Ancillaries:

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Lebesgue Integrable Functions
    • Chapter 2. Lebesgue’s Integral Compared to Riemann’s
    • Chapter 3. Function Spaces
    • Chapter 4. Measure Theory
    • Chapter 5. Hilbert Space Operators
  • Additional Material
     
     
  • Reviews
     
     
    • In 1902, modern function theory began when Henri Lebesgue described a new 'integral calculus.' His 'Lebesgue integral' handles more functions than the traditional integral--so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.

      Mathematical Reviews Clippings
    • When I noticed the title of this book, I was curious to see if this subject actually could be made comprehensible to an undergraduate. It turns out that it really can be, via a path to the Lebesgue integral that is different from the one I took as a graduate student. ... I like books that try something new, offer a different perspective on things, and are carefully and clearly written. This one qualifies on all counts. This is a book, I think, that students will actually read, and even better, enjoy.

      -Mark Hunacek, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 272015; 284 pp

This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text's use of a method labeled the “Daniell-Riesz approach.” The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist.

Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions.

Ancillaries:

  • Chapters
  • Introduction
  • Chapter 1. Lebesgue Integrable Functions
  • Chapter 2. Lebesgue’s Integral Compared to Riemann’s
  • Chapter 3. Function Spaces
  • Chapter 4. Measure Theory
  • Chapter 5. Hilbert Space Operators
  • In 1902, modern function theory began when Henri Lebesgue described a new 'integral calculus.' His 'Lebesgue integral' handles more functions than the traditional integral--so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.

    Mathematical Reviews Clippings
  • When I noticed the title of this book, I was curious to see if this subject actually could be made comprehensible to an undergraduate. It turns out that it really can be, via a path to the Lebesgue integral that is different from the one I took as a graduate student. ... I like books that try something new, offer a different perspective on things, and are carefully and clearly written. This one qualifies on all counts. This is a book, I think, that students will actually read, and even better, enjoy.

    -Mark Hunacek, MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.