Elementary introduction to the Lebesgue integral (Record no. 211353)

000 -LEADER
fixed length control field cam a22 i 4500
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 190401b 2018 ||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781138482760
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.43
Item number K7E5
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Krantz, Steven G.
Dates associated with a name
9 (RLIN) 376202
245 ## - TITLE STATEMENT
Title Elementary introduction to the Lebesgue integral
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc New York
Name of publisher, distributor, etc CRC Press
Date of publication, distribution, etc 2018
300 ## - PHYSICAL DESCRIPTION
Extent xii, 183p.
Other physical details With index
440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Textbooks in Mathematics
9 (RLIN) 377167
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc 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
520 ## - SUMMARY, ETC.
Summary, etc 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

650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Lebesgue integral
Form subdivision Textbooks.
9 (RLIN) 376203
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Integrals, Generalized
Form subdivision Textbooks.
9 (RLIN) 376204
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Measure theory
Form subdivision Textbooks.
9 (RLIN) 376205
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Permanent location Current location Shelving location Date acquired Source of acquisition Cost, normal purchase price Item location Full call number Barcode Date last seen Cost, replacement price Koha item type
          Non-fiction Vikram Sarabhai Library Vikram Sarabhai Library General Stacks 2019-03-28 13 4.00 Slot 1377 (0 Floor, East Wing) 515.43 K7E5 198919 2019-03-28 5220.83 Books

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