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测度论（第一卷）（影印版）

样章
作者：
V.I. Bogachev
定价：
55.80元
ISBN：
978-7-04-028696-0
版面字数：
510.000千字
开本：
16开
全书页数：
500页
装帧形式：
平装
重点项目：
暂无
出版时间：
2010-07-09
物料号：
28696-00
读者对象：
高等教育
一级分类：
数学与统计学类
二级分类：
数学与统计学类其他课程
三级分类：
其他课程
暂无
  • 前辅文
  • Chapter 1. Constructions and extensions of measur
    • 1.1. Measurement of length: introductory rema
    • 1.2. Algebras and σ-algebras
    • 1.3. Additivity and countable additivity of measur
    • 1.4. Compact classes and countable additivit
    • 1.5. Outer measure and the Lebesgue extension of measur
    • 1.6. Infinite and σ-finite measure
    • 1.7. Lebesgue measu
    • 1.8. Lebesgue-Stieltjes measur
    • 1.9. Monotone and σ-additive classes of se
    • 1.10. Souslin sets and the A-operat
    • 1.11. Caratheodory outer measure
    • 1.12. Supplements and exerci
  • Chapter 2. The Lebesgue integra
    • 2.1. Measurable functio
    • 2.2. Convergence in measure and almost everywh
    • 2.3. The integral for simple functio
    • 2.4. The general definition of the Lebesgue integra
    • 2.5. Basic properties of the integr
    • 2.6. Integration with respect to infinite measur
    • 2.7. The completeness of the space
    • 2.8. Convergence theorem
    • 2.9. Criteria of integrabil
    • 2.10. Connections with the Riemann integr
    • 2.11. The H¨older and Minkowski inequalit
    • 2.12. Supplements and exercis
  • Chapter 3. Operations on measures and functio
    • 3.1. Decomposition of signed measu
    • 3.2. The Radon–Nikodym theor
    • 3.3. Products of measure spac
    • 3.4. Fubini’s theore
    • 3.5. Infinite products of measur
    • 3.6. Images of measures under mappin
    • 3.7. Change of variables in I
    • 3.8. The Fourier transfor
    • 3.9. Convoluti
    • 3.10. Supplements and exercis
  • Chapter 4. The spaces Lp and spaces of measure
    • 4.1. The spaces
    • 4.2. Approximations in Lp
    • 4.3. The Hilbert space
    • 4.4. Duality of the spaces
    • 4.5. Uniform integrabilit
    • 4.6. Convergence of measu
    • 4.7. Supplements and exercis
  • Chapter 5. Connections between the integral and derivativ
    • 5.1. Differentiability of functions on the real lin
    • 5.2. Functions of bounded variatio
    • 5.3. Absolutely continuous function
    • 5.4. The Newton–Leibniz formula
    • 5.5. Covering theore
    • 5.6. The maximal funct
    • 5.7. The Henstock–Kurzweil integra
    • 5.8. Supplements and exercis
  • Bibliographical and Historical Commen
  • Reference
  • Author Inde
  • Subject Inde

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