《歐氏空間上的勒貝格積分（修訂版）》是2018年世界圖書出版公司出版的著作，作者是Frank、Jones 。
基本介紹
- 中文名：《歐氏空間上的勒貝格積分（修訂版）》
- 作者：Frank、Jones
- 出版社：世界圖書出版公司
- 出版時間：2018年10月01日
- ISBN：9787519248505
內容簡介,作者簡介,
內容簡介
The treatment ofintegration developed by the French mathematician Henri Lebesgue （1875-1944） almost a century ago has proved to be indispensable in many areas of mathematics. Lebesgue's theory is of such extreme importance because on the one hand it has rendered previous theories of integration virtually obsolete， and on the other hand it has not been replaced with a sigruficantly different， better theory. Most subsequent important investigations of integration theory have extended or illuminated Lebesgue's work.
In fact， as is so often the case in a new field of mathematics， many of the best consequences were given by the originator. For example， Lebesgue's dominated convergence theorem， Lebesgue's increasing convergence theorem， the theory of the Lebesgue function of the Cantor ternary set， and Lebesgue's theory of differentiation of indefinite integrals.
Naturally， many splendid textbooks have been produced in this area. I shall list some of these below. They are quite varied in their approach to the subject. My aims in the present book are as follows.
1. To present a 81ow introduction to Lebesgue integration. Most books nowadays take the opposite tack. I have no argument with their approach， except that I feel that many students who see only a very rapid approach tend to lack strong intuition about measure and integration. That is why I have made Chapter 2， "Lebesgue measure on Rn，" so lengthy and have restricted it to Euclidean space， and why I have （somewhat inconveniently） placed Chapter 3， "Invariance of Lebesgue measure，" before Fubini's theorem. In my approach I have omitted much important material， for the sake of concreteness. As the title of the book signifies， I restrict attention almost entirely to Euclidean space.
2. To deal with n-dimensional spaces from the outset. I believe this is preferable to one standard approach to the theory which first thoroughly treats integration on the real line and then generalizes. There are several reasons for this belief. One is quite simply that significant figures are frequently easier to sketch in R2 than in R1! Another is that some things in R1 are so special that the generalization to Rn is not clear， for example， the structure of the most general open set in R is essentially trivial - it must be a disjoint union of open intervals （see Problem 2.6）. A third is that coping with the n-dimensional case from the outset causes the learner to realize that it is not significantly more difficult than the one-dimensional case as far as many aspects of integration are concerned.
作者簡介
本書作者是Frank Jones（F.瓊斯）美國美國德克薩斯州的萊斯大學（Rice University）教授，該校是一所世界著名的私立研究型大學，“新常春藤”名校之一。
