实分析入门（修订版） Introductory Real Analysis (Revised)

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 416 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486612263

Published:1 Feb 2000

Weight:484g

Dimensions:206 x 140 x 22 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

理查德·西尔弗曼翻译的俄文数学著作系列中的这一卷，是莫斯科大学两位教员对实数和函数分析的齐全、基础介绍。这本书内容丰富、节奏均匀、易读性强，对于那些在高等微积分方面有充分准备的人来说很容易理解。

前四章介绍了集合论、度量空间、拓扑空间和线性空间的基本概念和入门原理。接下来的两章讨论了线性泛函和线性算子，详细讨论了连续线性泛函、共轭空间、弱拓扑和弱收敛、广义函数、线性算子的基本概念、逆算子和伴随算子以及完全连续算子。后四章涵盖了测度、积分、微分以及有关积分的更多内容。这里特别关注了勒贝斯克积分、富比尼定理和斯蒂尔杰斯积分。每个部分（总共 37 个）都配有一套习题，总共约 350 道习题，所有习题都经过精心挑选和匹配。

本书的问题和清晰的阐述，对于自学或课堂教学都很有用——它是实分析的基础一年制课程。Silverman 博士曾是纽约大学数学科学研究所和麻省理工学院林肯图书馆的成员。除了翻译之外，他还对文本进行了大量的教学和数学改进，并重新设计了语言，使其更具可读性。

This volume in Richard Silverman's exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus.

The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.

With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.

作者简介

安德雷·尼古拉耶维奇·柯尔莫哥洛夫，俄国数学家，主要研究概率论、算法信息论、拓扑学、直觉主义逻辑、紊流、经典力学和计算复杂性理论，颇为人所道的是对概率论公理化所作出的贡献。他曾说：“概率论作为数学学科，可以而且应该从公理开始建设，和几何、代数的路一样”。

Andrey Nikolayevich Kolmogorov, a Russian mathematician, mainly studies probability theory, algorithmic information theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity theory. He is best known for his contribution to the axiomatization of probability theory. He once said: "Probability theory, as a mathematical discipline, can and should be built from axioms, just like geometry and algebra."