| 书目名称 | Lectures on Functional Analysis and the Lebesgue Integral | | 编辑 | Vilmos Komornik | | 视频video | | | 概述 | Develops functional analysis in an original way, motivated by natural examples of plane geometry.Provides many examples and counterexamples to help the reader understand the meaning, usefulness and op | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | .This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small ℓ.p. spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým...Lectures on Functional Analysis and the Lebesgue Integral. presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they arecombined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included...Both undergraduate and graduate students in pure and applied mathematics, physi | | 出版日期 | Textbook 2016 | | 关键词 | Functional analysis; Hilbert space; normed space; Banach space; dual space; weak convergence; reflexivity; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4471-6811-9 | | isbn_softcover | 978-1-4471-6810-2 | | isbn_ebook | 978-1-4471-6811-9Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag London 2016 |
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发表于 2025-3-21 18:38:38
