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Elementary introduction to the Lebesgue integral / Steven G. Krantz.

By: Krantz, Steven G [author.].
Material type: materialTypeLabelBookSeries: Textbooks in Mathematics.Publisher: Boca Raton, FL : CRC Press, [2018]Copyright date: ©2018Edition: First edition.Description: 1 online resource (xii, 183 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9781351056793; 9781351056823.Subject(s): Lebesgue integralAdditional physical formats: Print version:: No titleDDC classification: 515.42 Online resources: Click here to view.
Contents:
chapter 1 Introductory Thoughts / Steven G. Krantz -- chapter 2 The Purpose of Measures / Steven G. Krantz -- chapter 3 The Leuesgue Integral / Steven G. Krantz -- chapter 4 Integrable Functions / Steven G. Krantz -- chapter 5 The Lebesgue Spaces / Steven G. Krantz -- chapter 6 The Concept of Outer Measure / Steven G. Krantz -- chapter 7 What Is a Measurable Set? / Steven G. Krantz -- chapter 8 Decomposition Theorems / Steven G. Krantz -- chapter 9 Creation of Measures / Steven G. Krantz -- chapter 10 Instances of Measurable Sets / Steven G. Krantz -- chapter 11 Approximation by Open And Closed Sets / Steven G. Krantz -- chapter 12 Different Methods of Convergence / Steven G. Krantz -- chapter 13 Measure on a Product Space / Steven G. Krantz -- chapter 14 Additivity for Outer Measure / Steven G. Krantz -- chapter 15 Nonmeasuraule Sets and Non‐Borel Sets / Steven G. Krantz -- chapter 16 Applications / Steven G. Krantz.
Summary: "It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a device for amalgamating information. It is a powerful and irreplaceable tool. The text concentrates on the real line. The student will be familiar with the real numbers and will be comfortable internalizing the new ideas of measure theory in that context. In addition to having copious examples and numerous figures, this book includes a Table of Notation and a Glossary."--Provided by publisher.
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chapter 1 Introductory Thoughts / Steven G. Krantz -- chapter 2 The Purpose of Measures / Steven G. Krantz -- chapter 3 The Leuesgue Integral / Steven G. Krantz -- chapter 4 Integrable Functions / Steven G. Krantz -- chapter 5 The Lebesgue Spaces / Steven G. Krantz -- chapter 6 The Concept of Outer Measure / Steven G. Krantz -- chapter 7 What Is a Measurable Set? / Steven G. Krantz -- chapter 8 Decomposition Theorems / Steven G. Krantz -- chapter 9 Creation of Measures / Steven G. Krantz -- chapter 10 Instances of Measurable Sets / Steven G. Krantz -- chapter 11 Approximation by Open And Closed Sets / Steven G. Krantz -- chapter 12 Different Methods of Convergence / Steven G. Krantz -- chapter 13 Measure on a Product Space / Steven G. Krantz -- chapter 14 Additivity for Outer Measure / Steven G. Krantz -- chapter 15 Nonmeasuraule Sets and Non‐Borel Sets / Steven G. Krantz -- chapter 16 Applications / Steven G. Krantz.

"It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a device for amalgamating information. It is a powerful and irreplaceable tool. The text concentrates on the real line. The student will be familiar with the real numbers and will be comfortable internalizing the new ideas of measure theory in that context. In addition to having copious examples and numerous figures, this book includes a Table of Notation and a Glossary."--Provided by publisher.

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