Introduction to Real Analysis. 1st ed. 2019

種類:

電子ブック

責任表示:

by Christopher Heil

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Heil, Christopher.
• SpringerLink (Online service)

シリーズ名:

Graduate Texts in Mathematics ; 280

ISBN:

9783030269036 [3030269035]    

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 understandi

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