Real analysis. Modern techniques and their applications. 2nd ed.

*(English)*Zbl 0924.28001See also the review of the first edition (1984) in Zbl 0549.28001.

From the Preface of the second edition: The new features of this edition are as follows:

\(\bullet\) The material on the \(n\)-dimensional Lebesgue integral has been rearranged and expanded.

\(\bullet\) Tychonoff’s theorem is proved by an elegant argument recently discovered by Paul Chernoff.

\(\bullet\) The chapter on Fourier analysis has been split into two chapters.

The material on Fourier series and integrals has been rearranged and now contains the Dirichlet-Jordan theorem on convergence of Fourier series.

The material on distributions has been extensively rewritten and expanded.

\(\bullet\) A section on self-similarity and Hausdorff dimension has been added, replacing the outdated calculation of the Hausdorff dimension of Cantor sets in the old one.

\(\bullet\) Innumerable small changes have been made in the hope of improving the exposition.

From the Preface of the second edition: The new features of this edition are as follows:

\(\bullet\) The material on the \(n\)-dimensional Lebesgue integral has been rearranged and expanded.

\(\bullet\) Tychonoff’s theorem is proved by an elegant argument recently discovered by Paul Chernoff.

\(\bullet\) The chapter on Fourier analysis has been split into two chapters.

The material on Fourier series and integrals has been rearranged and now contains the Dirichlet-Jordan theorem on convergence of Fourier series.

The material on distributions has been extensively rewritten and expanded.

\(\bullet\) A section on self-similarity and Hausdorff dimension has been added, replacing the outdated calculation of the Hausdorff dimension of Cantor sets in the old one.

\(\bullet\) Innumerable small changes have been made in the hope of improving the exposition.

##### MSC:

28-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration |

28A25 | Integration with respect to measures and other set functions |

28A78 | Hausdorff and packing measures |

46-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis |

42-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces |

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |