中文名: 現代分析基礎
原名: Foundations of Modern Analysis Treatise On Analysis Vol-I
作者: J. Dieudonné
譯者: I. G. Macdonald
資源格式: DJVU
版本: 掃描版
出版社: Academic Press
書號: 0122155084
發行時間: 1969年
地區: 美國
語言: 英文
簡介:

內容簡介：
J.Dieudonne是法國布爾巴基學派的重要級人物，在 1960 到 1982 出版的他的 Treatise on Analysis 多卷本， 英譯本由 I.G.Macdonald 翻譯並由 Academic Press 出版，該書堪稱分析方面史詩般的著作，是分析方面的百科全書。
FOUNDATIONS OF MODERN ANALYSIS. Enlarged and Corrected Printing J. DIEUDONNE This book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentially without changes, of my Foundations of Modern Analysis. Many readers, colleagues, and friends have urged me to write a sequelto that book, and in the end I became convinced that there was a place fora survey of modern analysis, somewhere between the minimum tool kitof an elementary nature which I had intended to write, and specialist monographs leading to the frontiers of research. My experience of teachinghas also persuaded me that the mathematical apprentice, after taking the firststep of Foundations, needs further guidance and a kind of general birdseye view of his subject before he is launched onto the ocean of mathematical literature or set on the narrow path of his own topic of research.Thus I have finally been led to attempt to write an equivalent, for the mathematicians of 1970, of what the Cours dAnalyse of Jordan, Picard,and Goursat were for mathematical students between 1880 and 1920.It is manifestly out of the question to attempt encyclopedic coverage, and certainly superfluous to rewrite the works of N. Bourbaki. I have therefore been obliged to cut ruthlessly in order to keep within limits comparable tothose of the classical treatises. I have opted for breadth rather than depth, inthe opinion that it is better to show the reader rudiments of many branchesof modern analysis rather than to provide him with a complete and detailedexposition of a small number of topics.Experience seems to show that the student usually finds a new theorydifficult to grasp at a first reading. He needs to return to it several times beforehe becomes really familiar with it and can distinguish for himself whichare the essential ideas and which results are of minor importance, and onlythen will he be able to apply it intelligently. The chapters of this treatise are therefore samples rather than complete theories: indeed, I have systematically tried not to be exhaustive. The works quoted in the bibliography willalways enable the reader to go deeper into any particular theory.However, I have refused to distort the main ideas of analysis by presentingthem in too specialized a form, and thereby obscuring their power andgenerality. It gives a false impression, for example, if differential geometryis restricted to two or three dimensions, or if integration is restricted to Lebesgue measure, on the pretext of making these subjects more accessible orintuitive.On the other hand I do not believe that the essential content of the ideasinvolved is lost, in a first study, by restricting attention to separable metrizabletopological spaces. The mathematicians of my own generation were certainlyright to banish, hypotheses of countability wherever they were not needed: thiswas the only way to get a clear understanding.
內容截圖：

目錄:
Treatise On Analysis
10-I Chapters I-XI
10-II Chapters XII-XV
10-III Chapters XVI-XVII
10-IV Chapters XVIII-XX
10-V Chapter XXI
10-VI Chapter XXII
10-VIII Chapter XXIII,Part II