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Elementary introduction to the Lebesgue integral

By: Krantz, Steven G, .
Material type: materialTypeLabelBookSeries: Textbooks in Mathematics. Publisher: New York CRC Press 2018Description: xii, 183p. With index.ISBN: 9781138482760.Subject(s): Lebesgue integral -- Textbooks | Integrals, Generalized -- Textbooks | Measure theory -- TextbooksDDC classification: 515.43 Summary: Elementary Introduction to the Lebesgue Integral is not just an excellent primer of the Lebesgue integral for undergraduate students but a valuable tool for tomorrow’s mathematicians. Since the early twentieth century, the Lebesgue integral has been a mainstay of mathematical analysis because of its important properties with respect to limits. For this reason, it is vital that mathematical students properly understand the complexities of the Lebesgue integral. However, most texts about the subject are geared towards graduate students, which makes it a challenge for instructors to properly teach and for less advanced students to learn. Ensuring that the subject is accessible for all readers, the author presents the text in a clear and concrete manner which allows readers to focus on the real line. This is important because Lebesgue integral can be challenging to understand when compared to more widely used integrals like the Riemann integral. The author also includes in the textbook abundant examples and exercises to help explain the topic. Other topics explored in greater detail are abstract measure spaces and product measures, which are treated concretely. Features: Comprehensibly written introduction to the Lebesgue integral for undergraduate students Includes many examples, figures and exercises Features a Table of Notation and Glossary to aid readers Solutions to selected exercises
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Slot 1377 (0 Floor, East Wing) Non-fiction 515.43 K7I6 (Browse shelf) Not for Issue 198919

TABLE OF CONTENTS
Chapter 1
Introductory Thoughts
BySteven G. Krantz

Chapter 2
The Purpose of Measures
BySteven G. Krantz

Chapter 3
The Leuesgue Integral
BySteven G. Krantz

Chapter 4
Integrable Functions
BySteven G. Krantz

Chapter 5
The Lebesgue Spaces
BySteven G. Krantz

Chapter 6
The Concept of Outer Measure
BySteven G. Krantz

Chapter 7
What Is a Measurable Set?
BySteven G. Krantz

Chapter 8
Decomposition Theorems
BySteven G. Krantz

Chapter 9
Creation of Measures
BySteven G. Krantz

Chapter 10
Instances of Measurable Sets
BySteven G. Krantz

Chapter 11
Approximation by Open And Closed Sets
BySteven G. Krantz

Chapter 12
Different Methods of Convergence
BySteven G. Krantz

Chapter 13
Measure on a Product Space
BySteven G. Krantz

Chapter 14
Additivity for Outer Measure
BySteven G. Krantz

Chapter 15
Nonmeasuraule Sets and Non‐Borel Sets
BySteven G. Krantz

Chapter 16
Applications
BySteven G. Krantz

Elementary Introduction to the Lebesgue Integral is not just an excellent primer of the Lebesgue integral for undergraduate students but a valuable tool for tomorrow’s mathematicians. Since the early twentieth century, the Lebesgue integral has been a mainstay of mathematical analysis because of its important properties with respect to limits. For this reason, it is vital that mathematical students properly understand the complexities of the Lebesgue integral. However, most texts about the subject are geared towards graduate students, which makes it a challenge for instructors to properly teach and for less advanced students to learn.
Ensuring that the subject is accessible for all readers, the author presents the text in a clear and concrete manner which allows readers to focus on the real line. This is important because Lebesgue integral can be challenging to understand when compared to more widely used integrals like the Riemann integral. The author also includes in the textbook abundant examples and exercises to help explain the topic. Other topics explored in greater detail are abstract measure spaces and product measures, which are treated concretely.
Features:
Comprehensibly written introduction to the Lebesgue integral for undergraduate students
Includes many examples, figures and exercises
Features a Table of Notation and Glossary to aid readers
Solutions to selected exercises

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