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Analysis Real Analysis by Stein and Shakarchi

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  1. Jan 25, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Foreword
    [*] Introduction
    [LIST]
    [*] Fourier series: completion
    [*] Limits of continuous functions
    [*] Length of curves
    [*] Differentiation and integration
    [*] The problem of measure
    [/LIST]
    [*] Measure Theory
    [LIST]
    [*] Preliminaries
    [*] The exterior measure
    [*] Measurable sets and the Lebesgue measure
    [*] Measurable functions
    [LIST]
    [*] Definition and basic properties
    [*] Approximation by simple functions or step functions
    [*] Littlewoord's three principles
    [/LIST]
    [*] The Brunn-Minkowski inequality
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Integration Theory
    [LIST]
    [*] The Lebesgue integral: basic properties and convergence theorems
    [*] The space L^1 of integrable functions
    [*] Fubini's theorem
    [LIST]
    [*] Statement and proof of the theorem
    [*] Applications of Fubini's theorem
    [/LIST]
    [*] A Fourier inversion formula
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Differentiation and Integration
    [LIST]
    [*] Differentiation of the integral
    [LIST]
    [*] The Hardy-Littlewood maximal function
    [*] The Lebesgue differentiation theorem
    [/LIST]
    [*] Good kernels and approximations to the identity
    [*] Differentiability of functions
    [LIST]
    [*] Functions of bounded variation
    [*] Absolutely continuous functions
    [*] Differentiability of jump functions
    [/LIST]
    [*] Rectifiable curves and the isoperimetric inequality
    [LIST]
    [*] Minkowski content of a curve
    [*] Isoperimetric inequality
    [/LIST]
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Hilbert Spaces: An Introduction
    [LIST]
    [*] The Hilbert space L^2
    [*] Hilbert spaces
    [LIST]
    [*] Orthogonality
    [*] Unitary mappings
    [*] Pre-Hilbert spaces
    [/LIST]
    [*] Fourier series and Fatou's theorem
    [LIST]
    [*] Fatou's theorem
    [/LIST]
    [*] Closed subspaces and orthogonal projections
    [*] Linear transformations
    [LIST]
    [*] Linear functionals and the Riesz representation theorem
    [*] Adjoints
    [*] Examples
    [/LIST]
    [*] Compact operators
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Hilbert Spaces: Several Examples
    [LIST]
    [*] The Fourier transform on L^2
    [*] The Hardy space of the upper half-plane
    [*] Constant coefficient partial differential equations
    [LIST]
    [*] Weak solutions
    [*] The main theorem and key estimate
    [/LIST]
    [*] The Dirichlet principle
    [LIST]
    [*] Harmonic functions
    [*] The boundary value problem and Dirichlet's principle
    [/LIST]
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Abstract Measure and Integration Theory
    [LIST]
    [*] Abstract measure spaces
    [LIST]
    [*] Exterior measures and Caratheodory's theorem
    [*] Metric exterior measures
    [*] The extension theorems
    [/LIST]
    [*] Integration on a measure space
    [*] Examples
    [LIST]
    [*] Product measures and a general Fubini theorem
    [*] Integration formula for polar coordinates
    [*] Borel measures on R and the Lebesgue-Stieltjes integral
    [/LIST]
    [*] Absolute continuity of measures
    [LIST]
    [*] Signed measures
    [*] Absolute continuity
    [/LIST]
    [*] Ergodic theorems
    [LIST]
    [*] Mean ergodic theorem
    [*] Maximal ergodic theorem
    [*] Pointwise ergodic theorem
    [*] Ergodic measure-preserving transformations
    [/LIST]
    [*] Appendix: the spectral theorem
    [LIST]
    [*] Statement of the theorem
    [*] Positive operators
    [*] Proof of the theorem
    [*] Spectrum
    [/LIST]
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Hausdorff Measure and Fractals
    [LIST]
    [*] Hausdorff measure
    [*] Hausdorff dimension
    [LIST]
    [*] Examples
    [*] Self-similarity
    [/LIST]
    [*] Space-filling curves
    [LIST]
    [*] Quartic intervals and dyadic squares
    [*] Dyadic correspondence
    [*] Construction of the Peano mapping
    [/LIST]
    [*] Besicovitch sets and regularity
    [LIST]
    [*] The Radon transform
    [*] Regularity of sets when d\geq 3
    [*] Besicovitch sets have dimension 2
    [*] Construction of a Besicovtich set
    [/LIST]
    [*] Exercises
    [*] Problems
    [/LIST]
    [*] Notes and References
    [*] Bibliography
    [*] Symbol Glossary
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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