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Introduction to Real Analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to Real Analysis/ by Christopher Heil.
作者:	Heil, Christopher.
面頁冊數:	XXXII, 386 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Measure theory. -
電子資源:	https://doi.org/10.1007/978-3-030-26903-6
ISBN:	9783030269036

Introduction to Real Analysis
Heil, Christopher.

Introduction to Real Analysis[electronic resource] /by Christopher Heil. - 1st ed. 2019. - XXXII, 386 p. 1 illus.online resource. - Graduate Texts in Mathematics,2800072-5285 ;. - Graduate Texts in Mathematics,222.

Preliminaries -- 1. Metric and Normed Spaces -- 2. Lebesgue Measure -- 3. Measurable Functions -- 4. The Lebesgue Integral -- 5. Differentiation -- 6. Absolute Continuity and the Fundamental Theorem of Calculus -- 7. The L<i>p Spaces -- 8. Hilbert Spaces and L^2(E) -- 9. Convolution and the Fourier Transform.

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.

ISBN: 9783030269036

Standard No.: 10.1007/978-3-030-26903-6doiSubjects--Topical Terms:

527848
Measure theory.

LC Class. No.: QA312-312.5

Dewey Class. No.: 515.42

Introduction to Real Analysis
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