Fundamentals of Real Analysis / by Sterling K. Berberian
(Universitext)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1999 |
| 本文言語 | 英語 |
| 大きさ | XI, 479 p. 98 illus : online resource |
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| 一般注記 | Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis |
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| 著者標目 | *Berberian, Sterling K. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Functions of real variables FREE:Mathematics FREE:Real Functions |
| 分 類 | DC23:515.8 |
| 巻冊次 | ISBN:9781461205494 
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| ISBN | 9781461205494 |
| URL | http://dx.doi.org/10.1007/978-1-4612-0549-4 |
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