書目名稱 | Measure, Integration & Real Analysis | 編輯 | Sheldon Axler | 視頻video | http://file.papertrans.cn/629/628067/628067.mp4 | 概述 | Electronic version is free to the world via Springer’s Open Access program.Provides student-friendly explanations with ample examples and exercises throughout.Includes chapters on Hilbert space operat | 叢書名稱 | Graduate Texts in Mathematics | 圖書封面 |  | 描述 | .This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics..Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on .R.n...Chapters on Banach spaces, .L.p. spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, H?lder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for | 出版日期 | Textbook‘‘‘‘‘‘‘‘ 2020 | 關(guān)鍵詞 | Measure theory textbook; Graduate real analysis textbook; Open Access; Riemann integration; Lebesgue int | 版次 | 1 | doi | https://doi.org/10.1007/978-3-030-33143-6 | isbn_ebook | 978-3-030-33143-6Series ISSN 0072-5285 Series E-ISSN 2197-5612 | issn_series | 0072-5285 | copyright | Sheldon Axler 2020 |
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