| 書目名稱 | From Classical to Modern Analysis | | 編輯 | Rinaldo B. Schinazi | | 視頻video | http://file.papertrans.cn/349/348581/348581.mp4 | | 概述 | Guides undergraduate students from calculus to measure theory and the Lebesgue integral.Provides a self-contained presentation of metric spaces and their topology tailored for first-time students of r | | 圖書封面 |  | | 描述 | This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, .From Classical to Modern Analysis. is a comprehensive, yet straightforward, resource for studying real analysis..To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuityon metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral.?.Instructors who want to demonstrate the uses of measure theory and explore its | | 出版日期 | Textbook 2018 | | 關(guān)鍵詞 | Lebesgue integral; real analysis; measure theory; Euclidean spaces; metric spaces; numerical series; power | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-94583-5 | | isbn_softcover | 978-3-030-06879-0 | | isbn_ebook | 978-3-319-94583-5 | | copyright | Springer International Publishing AG, part of Springer Nature 2018 |
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