02873cam a2200181 i 4500008004500000020001800045082001700063100002500080245005300105260003000158300002700188440002900215504092600244520141701170650003402587650003902621650003102660190401b 2018 ||||| |||| 00| 0 eng d a9781138482760 a515.43bK7E5 aKrantz, Steven G.d aElementary introduction to the Lebesgue integral aNew YorkbCRC Pressc2018 axii, 183p.bWith index aTextbooks in Mathematics aTABLE 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 aElementary 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
aLebesgue integralvTextbooks. aIntegrals, GeneralizedvTextbooks. aMeasure theoryvTextbooks.