This textbook and treatise begins with classical real variables, systematically develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is based in a fascinating historical commentary interwoven into an exposition that includes perspectives with other fields.Comprehensive treatments include: the role of absolute continuity in differentiation and integration; the evolution of the Riesz representation theorem to Radon measures and distribution theory; weak convergence of measures and the DieudonnéGrothendieck theorem; and the deepest results in modern differentiation theory.Fundamental topics include: fractals and self-similarity; rearrangements and maximal functions; and the relation between surface and Hausdorff measures.There are hundreds of exercises ranging from routine to challenging. The self-contained presentation, including extensive appendices on functional and Fourier analysis, make this book ideal for the classroom, self-study, or professional reference.

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