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＜電子ブック＞
Introduction to Real Analysis / by Christopher Heil
(Graduate Texts in Mathematics. ISSN:21975612 ; 280)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2019
大きさ	XXXII, 386 p. 1 illus : online resource
著者標目	*Heil, Christopher author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Operator theory LCSH:Topology LCSH:Functional analysis LCSH:Fourier analysis FREE:Measure and Integration FREE:Operator Theory FREE:Topology FREE:Functional Analysis FREE:Fourier Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-26903-6

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