本书是以实变函数与泛函分析课程内容为先导的介绍近代实分析的引论性著作。除必要的基础知识外，一些最活跃的研究领域，如Calderen—Zygmund奇异积分算子，Hp空间的实变理论，算于的加权模不等式等，在书中都得到了充分反映．全书通过对实变量函数所构成的各种函数空间(如Lebesgue空间、连续函数空间、Hardy空间、BMO空间等)和它们之间的算子作用以及Fourier分析、算子与空间内插等重要方法的描述，对20世纪50年代以来逐步形成与发展的处理n维欧氏空间上各种分析问题的实变方法与技巧做了系统、深入、简明的介绍．本书内容丰富、近代、叙述严谨、简明，是实分析方面一本可读性很强的教科书与参考书．. 本书前4章可供本科高年级学生选修，全书可作基础与应用数学、计算数学等许多方面的研究生的公共学位课教材，为从事调和分析、偏微分方程、非线性分析、数值分析、乃至数学物理等方面的研究与应用的读者提供必要的实分析基础训练．...

《实分析习题集》(第2版)是优秀的实分析课程配套习题集．书中提供了600多道习题的详细解答。内容涉及实分析基础、拓扑和连续、测度论、Lebesgue积分、赋范空间与空间、Hilbcrt空间等．书后附录中列出了习题中引用的定理、引理等，因此不需要参考原书也能运用这本习题集。

《实分析(英文版·第4版)》是实分析课程的优秀教材，被国外众多著名大学（如斯坦福大学、哈佛大学等）采用。全书分为三部分：第一部分为实变函数论.介绍一元实变函数的勒贝格测度和勒贝格积分:第二部分为抽象空间。介绍拓扑空间、度量空间、巴拿赫空间和希尔伯特空间；第三部分为一般测度与积分理论。介绍一般度量空间上的积分.以及拓扑、代数和动态结构的一般理论。书中不仅包含数学定理和定义，而且还提出了富有启发性的问题，以便读者更深入地理解书中内容。

《实分析和概率论(原书第2版)》清晰地讲解了现代概率论以及概率测度与度量空间之间的相互关系。《实分析和概率论(原书第2版)》分两部分，第一部分介绍了实分析的内容，包括基础集合论、一般拓扑、测度、积分、巴拿赫空间及希尔伯特空间上的函数分析、凸集和函数以及拓扑空间上的测度，第二部分介绍了基于测度论卜的概率论，包括大数定律、遍历定理、中心极限定理、条件期望、鞅收敛另外，随机过程一章介绍了布朗运动以及布朗桥。

The first three editions of H．］．Royden’S Real Analysis have contributed to the education of generation so fm a them atical analysis students．This four the dition of Real Analysispreservesthe goal and general structure of its venerable predecessors——to present the measure theory．integration theory．and functional analysis that a modem analyst needs to know． The book is divided the three parts：Part I treats Lebesgue measure and Lebesgueintegration for functions of a single real variable；Part II treats abstract spaces topological spaces，metric spaces，Banach spaces，and Hilbert spaces；Part III treats integration over general measure spaces．together with the enrichments possessed by the general theory in the presence of topological，algebraic，or dynamical structure． The material in Parts II and III does not formally depend on Part I．However．a careful treatment of Part I provides the student with the opportunity to encounter new concepts in afamiliar setting，which provides a foundation and motivation for the more abstract conceptsdeveloped in the second and third parts．Moreover．the Banach spaces created in Part I．theLp spaces，are one of the most important dasses of Banach spaces．The principal reason forestablishing the completeness of the Lp spaces and the characterization of their dual spacesiS to be able to apply the standard tools of functional analysis in the study of functionals andoperators on these spaces．The creation of these tools is the goal of Part II．

An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

分析学（第2版），ISBN：9787040173819，作者：（美）利布、（美）洛斯

"Real Analysis" is the third volume in the "Princeton Lectures in Analysis", a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, "Real Analysis" is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.

《实变函数论与泛函分析:上册•第2版修订本》内容简介：本版保持了初版的思想体系和基本结构，从局部来看作了一定程度的修改。在编写初版时，我们对《实变函数论与泛函分析:上册•第2版修订本》编写的思想体系和基本结构给予了较多的考虑。但由于某些内容过去就很少有作为基础课讲授的教学经验，另一方面也由于当时编写时间比较仓促，因此从具体内容处理的技术方面来看，确有必要进行一次较全面的、细致的修订。本次修订，是在作者对初版进行了两次教学实践和兄弟院校使用初版后提出意见的基础上进行的。

《实分析》由在国际上享有盛誉普林斯大林顿大学教授Stein等撰写而成，是一部为数学及相关专业大学二年级和三年级学生编写的教材，理论与实践并重。为了便于非数学专业的学生学习，全书内容简明、易懂,读者只需掌握微积分和线性代数知识。关于《实分析》的详细介绍，请见“影印版前言”。

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

《实分析与复分析》(原书第3版)是分析领域内的一部经典著作。主要内容包括：抽象积分、正博雷尔测度、Lp-空间、希尔伯特空间的初等理论、巴拿赫空间技巧的例子、复测度、微分、积空间上的积分、傅里叶变换、全纯函数的初等性质、调和函数、最大模原理、有理函数逼近、共形映射、全纯函数的零点、解析延拓、Hp-空间、巴拿赫代数的初等理论、全纯傅里叶变换、用多项式一致逼近等。另外，书中还附有大量设计巧妙的习题。

《实变函数论(第2版)》是普通高等教育“九五”教育部重点教材，是为综合大学、理工科大学、高等师范院校数学系、应用数学系本科生编写的“实变函数”课程教材，主要介绍Lebesgue测度与积分理论、共分六章：集合与点集，Lebesgue测度,可测函数，Lebesgue积分，微分、不定积分，Lp空间等。作者30年来一直在北京大学讲授“实变函数”课，具有丰富的教学经验，且深知学生的疑难与困惑，因此《实变函数论(第2版)》在选材上对内容的难易程序，以及背景材料的选取都是作者经过深思熟虑安排的，是教学实践经验的总结，书中编有丰富的范例，为读者展示出广阔的应用空间。每章节后列入的精选思考题和数量众多的习题，又为读者提供了自我训练的恰当基地。作者在每章末尾所作的注记，拓宽或加深了正文所述的内容，这或许对有志于进一步学习实分析的读者有所助益。如果读者对近代积分论的前后发展感兴趣，还可阅读开篇“积分论评述”以及附录中的“Lebesgue传”。为便于读者学习，书后附中给出了部分思考题、课内练习题、课外精选题的解答，供教师和学生参考。

本书是分析领域内的一部经典著作。毫不夸张地说，掌握了本书，对数学的理解将会上一个新台阶。全书体例优美，实用性例优美，实用性很强，列举的实例简明精彩。无论实分析部分还是复分析部分，基本上对所有给出的命题都进行了论证。另外，书中还附有大量设计巧妙的习题——这些习题可以真实地检测出读者对课程的理解程序，有的还要求对正文中的原理进行论证。

实变函数论（第3版 第5版），ISBN：9787040292213，作者：（俄罗斯）那汤松 著，徐瑞云 译

强调严格性和基础性，书中的材料从源头——数系的结构及集合论开始，然后引向分析的基础(极限、级数、连续、微分、Riemann积分等)，再进入幂级数、多元微分学以及Fourier分析，最后到达Lebesgue积分，这些材料几乎完全是以具体的实直线和欧几里得空间为背景的。书中还包括关于数理逻辑和十进制系统的两个附录。课程的材料与习题紧密结合，目的是使学生能动地学习课程的材料，并且进行严格的思考和严密的书面表达的实践。