## Measure and Integral: An Introduction to Real Analysis, Second EditionNow considered a classic text on the topic, Published nearly forty years after the first edition, this long-awaited - Studies the Fourier transform of functions in the spaces
*L1*,*L2*, and*Lp*, 1 p - Shows the Hilbert transform to be a bounded operator on
*L2*, as an application of the*L2*theory of the Fourier transform in the one-dimensional case - Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation
- Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension
- Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient
- Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases
- Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables
- Includes many new exercises not present in the first edition
This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians. |

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### Contents

1 | |

Chapter 2 Functions of Bounded Variation and the RiemannStieltjes Integral | 17 |

Chapter 3 Lebesgue Measure and Outer Measure | 41 |

Chapter 4 Lebesgue Measurable Functions | 63 |

Chapter 5 The Lebesgue Integral | 81 |

Chapter 6 Repeated Integration | 113 |

Chapter 7 Differentiation | 129 |

Chapter 8 Lp Classes | 183 |

Chapter 10 Abstract Integration | 237 |

Chapter 11 Outer Measure and Measure | 279 |

Chapter 12 A Few Facts from Harmonic Analysis | 301 |

Chapter 13 The Fourier Transform | 371 |

Chapter 14 Fractional Integration | 415 |

Chapter 15 Weak Derivatives and PoincaréSobolev Estimates | 461 |

Notations | 501 |

Back Cover | 505 |

### Other editions - View all

Measure and Integral: An Introduction to Real Analysis, Second Edition Richard L. Wheeden No preview available - 2015 |