Measure and integral : theory and practice /
"This accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them. This material is typically covered in a grad...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press,
2025.
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| Edition: | Seventh edition. |
| Series: | Textbooks in mathematics (Boca Raton, Fla.)
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | "This accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them. This material is typically covered in a graduate course and is almost always treated in an abstract way, with little or no motivation. The author employs a plethora of examples and exercises and strives to motivate every concept with its historical background. This textbook is accessible to a wider range of students, including at the undergraduate level. A major problem facing anyone teaching measure theory is how to combine the elementary approach (measure on the real line or in the plane) and the abstract measure theory. The author develops a theory of measure in the plane, then show how to generalize these ideas to an abstract setting. The result is a textbook accessible to a wider range of students. The material requires a good understanding of topics often referred to as advanced calculus, such as Riemann integration on Euclidean spaces and series of functions. Also, a reader is expected to be proficient in the basics of set theory and point-set topology, preferably including metric spaces"-- |
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| Physical Description: | 1 online resource. |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: | 9781032712420 1032712422 9781040269398 1040269397 9781032716497 1032716495 9781040269428 1040269427 |