几何测度论

所属分类:数学  
出版时间:2004-11   出版时间:世界图书出版公司   作者:Herbert Federer   页数:676  
Tag标签:Mathematics,数学  

内容概要

This book aims to fill the need for a comprehensive treatise on geo-metric measure theory. It contains a detailed exposition leading from the foundations of the theory to the most recent discoveries, including many results not previously published. It is intended both as a reference book for mature mathematicians and as a textbook for able students. The material of Chapter 2 can be covered in a first year graduate course on real analysis. Study of the later chapters is suitable preparation for re-search. Some knowledge of elementary set theory, topology, linear algebra and commutative ring theory is prerequisite for reading this book, but the treatment is selfcontained with regard to all those topics in multilinear algebra, analysis, differential geometry and algebraic topology which occur.

作者简介

Herbert Federer was born on July 23, 1920, in Vienna. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley. Affiliated to Brown University, Providence since 1945, he is now Professor Emeritus there.
The major part of Professor Federer's scientific effort has been directed to the development of the subject of Geometric Measure Theory, with its roots and applications in classical geometry and analysis, yet in the functorial spirit of modern topology and algebra. His work includes more than thirty research papers published between 1943 and 1986, as well as this book.

书籍目录

IntroductionCHAPTER
ONE
Grassmann
algebra
1.1.
Tensor
products
1.2.
Graded
algebras
1.3.
The
exterior
algebra
of
a
vectorspace
1.4.
Alternating
forms
and
duality
1.5.
Interior
multiplications
1.6.
Simple
m-vectors
1.7.
Inner
products
1.8.
Mass
and
comass
1.9.
The
symmetric
algebra
of
a
vectorspace
1.10.
Symmetric
forms
and
polynomial
functionsCHAPTER
TWO
General
measure
theory
2.1.
Measures
and
measurable
sets
2.1.1.
Numerical
summation
2.1.2.-3.
Measurable
sets
2.1.4.-5.
Measure
hulls
2.1.6.
Ulam
numbers
2.2.
Borel
and
Suslin
sets
2.2.1.
Borel
families
2.2.2.
-3.
Approximation
lay
closed
subsets
2.2.4.
-5.
Nonmeasurable
sets
2.2.5.
Radon
measures
2.2.6.
The
space
of
sequences
of
positive
integers
2.2.7.
-9.
Lipschitzian
maps
2.2.10.-13.
Suslin
sets
2.2.14.-15.
Borel
and
Baire
functions
2.2.16.
Separability
of
supports
2.2.17.
Images
of
Radon
measures
2.3
Measurable
functions
2.3.1.-2.
Basic
properties
2.3.3.-7.
Approximation
theorems
2.3.8.-10.
Spaces
of
measurable
functions
2.4.
Lebesgue
integration
2.4.1.-5.
Basic
properties
2.4.6.-9.
Limit
theorems
2.4.10.-11.
Integrals
over
subsets
2.4.12.-17.
Lebesgue
spaces
2.4.18.
Compositions
and
image
measures
2.4.19.
Jensen''s
inequality
2.5.
Linear
functionals
2.5.1.
Lattices
of
functions
2.5.2.-6.
Daniell
integrals
2.5.7.-12.
Linear
functionals
on
Lebesgue
spaces
2.5.13.-15.
Riesz''s
representation
theorem
2.5.16.
Curve
length
……CHAPTER
THREE
RectifiabilityCHAPTER
FOUR
Homological
integration
theoryCHAPTER
FIVE
Applications
to
the
calculus
of
variationsBibliographyGlossary
of
some
standrd
notationsList
of
basic
notations
defined
in
the
textIndex

图书封面

图书标签Tags

Mathematics,数学


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用户评论 (总计24条)

 
 

  •     内容丰富,可以当字典收藏
  •     相当经典的教材,现在正在读呢!
  •     怎一个难字了得
  •     看吧!学吧!学完就成仙了!
  •     很实用的考试书,希望有帮助。
  •     但是有些还需要慢慢琢磨,不适合普通的小学生读
  •     感觉很不错。尤其不是教科书式的讲解,书没问题
  •     里面的方法总结给我帮助很大,学习数学课外用书
  •     有点读不进去- -但是应该是本很好的书,没想到那么薄啊
  •     我刚买了一本3.孩子很喜欢,物流和服务都很好
  •     很适合高中生用的辅导书。,不是传统意义上的学数学解题方法的书。延展的非常好。一年级的孩子很喜欢。
  •     正准备学习,适合边学边做
  •     经典啊,内容不错~就是价格太高
  •     封面没有破损。内容还没看完。,复习用书
  •     数学描红本,结果让我买了个05版的。希望能及时上新版。
  •     书很好也很便宜,还要配合其他的线代书看看
  •     课件制作的很好,学数理统计用的
  •     作者对内容有深刻理解,但还是能够借鉴的。
  •     自己看着都想做哈,可以学习学习!
  •     对我很有作用,内容刘畅!
  •     希望自己考研顺利,为了学哲学
  •     不过纸质不怎么好。,这本书的解析很不错
  •     如能再附上一些完整的工具箱就更好了。,帮朋友捎的书
  •     买回来才知道里面是10以内加减法的习题,送货也挺快的。赞一个
 

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