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    • 欧氏空间上的勒贝格积分(修订版)(英文版)
      • 作者:(美)F.琼斯
      • 出版社:世界图书出版公司
      • ISBN:9787519248505
      • 出版日期:2018/10/01
      • 页数:588
    • 售价:51.6
  • 内容大纲

        F.琼斯著的《欧氏空间上的勒贝格积分(修订版)(英文版)》从4个方面详细介绍勒贝格测度和Rn上的积分,具体包括勒贝格积分,n维空间,傅里叶积分,实分析。贯穿全书的大量练习可以增强读者对知识的理解。
  • 作者介绍

  • 目录

    Preface
    Bibliography
    Acknowledgments
    1 Introduction to Rn
    A Sets
    B Countable Sets
    C Topology
    D Compact Sets
    E Continuity
    F The Distance Function
    2 Lebesgue Measure on Rn
    A Construction
    B Properties of Lebesgue Measure
    C Appendix: Proof of P1 and P2
    3 Invariance of Lebesgue Measure
    A Some Linear Algebra
    B Translation and Dilation
    C Orthogonal Matrices
    D The General Matrix
    4 Some Interesting Sets
    A A Nonmeasurable Set
    B A Bevy of Cantor Sets
    C The Lebesgue Function
    D Appendix: The Modulus of Continuity
    of the Lebesgue Functions
    5 Algebras of Sets and Measurable Functions
    A Algebras and a-Algebras
    B Borel Sets
    C A Measurable Set which Is Not a Borel Set
    D Measurable Functions
    E Simple Functions
    6 Integration
    A Nonnegative Functions
    B General Measurable Functions
    C Almost Everywhere
    D Integration Over Subsets of Rn
    E Generalization: Measure Spaces
    F Some Calculations
    G Miscellany
    7 Lebesgue Integral on n
    A Riemann Integral
    B Linear Change of Variables
    C Approximation of Functions in L1
    D Continuity of Translation in L1
    8 Fubini's Theorem for Rn
    9 The Gamma Function
    A Definition and Simple Properties
    B Generalization
    C The Measure of Balls
    D Further Properties of the Gamma Function

    E Stirling's Formula
    F The Gamma Function on
    10 LP Spaces
    A Definition and Basic Inequalities
    B Metric Spaces and Normed Spaces
    C Completeness of Lp
    D The Case p = cc
    E Relations between Lp Spaces
    F Approximation by C (R)
    G Miscellaneous Problems
    H The Case 0 < p < 1
    11 A Products of a-Algebras
    B Monotone Classes
    C Construction of the Product Measure
    D The Fubini Theorem
    E The Generalized Minkowski Inequality
    12 Convolutions
    A Formal Properties
    B Basic Inequalities
    C Approximate Identities
    13 Fourier Transform on Rn
    A Fourier Transform of Functions in LI(R)
    B The Inversion Theorem
    C The Schwartz Class
    D The Fourier-Plancherel Transform
    E Hilbert Space
    F Formal Application to Differential Equations
    G Bessel Functions
    H Special Results for n = 1
    I Hermite Polynomials
    14 Fourier Series in One Variable
    A Periodic Functions
    B Trigonometric Series
    C Fourier Coefficients
    D Convergence of Fourier Series
    E Summability of Fourier Series
    F A Counterexample
    G Parseval's Identity
    H Poisson Summation Formula
    I A Special Class of Sine Series
    15 Differentiation
    A The Vitali Covering Theorem
    B The Hardy-Littlewood Maximal Function
    C Lebesgue's Differentiation Theorem
    D The Lebesgue Set of a Function
    E Points of Density
    F Applications
    G The Vitali Covering Theorem (Again)
    H The Besicovitch Covering Theorem
    I The Lebesgue Set of Order p

    J Change of Variables
    K Noninvertible Mappings
    16 Differentiation for Functions on R
    A Monotone Functions
    B Jump Functions :
    C Another Theorem of Fubini :
    D Bounded Variation
    E Absolute Continuity
    F Further Discussion of Absolute Continuity
    G Arc Length
    H Nowhere Differentiable Functions
    I Convex Functions
    Index
    Symbol Index

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