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Real analysis. (English) Zbl 0872.26001
International Edition. Upper Saddle River, NJ: Prentice-Hall International. xiv, 713 p. (1997).
The authors describe: measures and signed measures, the Lebesgue measure, metric outer measures, Hausdorff measures, integrations (of Newton, Cauchy, Riemann, Lebesgue, Stieltjes and Henstock-Kurzweil), Fubini’s theorem, the differentiation of functions, \(VCB_*\) functions, the approximate continuity and the Lebesgue points, the differentiation of measures, the differentiation basis in \(\mathbb{R}^n\), Radon-NikodĂ˝m derivatives in measure spaces, some metric spaces, Banach spaces, the Hahn-Banach theorem, the Baire category theorem, analytic sets, the contraction mapping principle, Ascoli’s theorem, \(L^p\) spaces and Fourier series. The exercises sections represent an important part of the book.
The book is suitable for students in mathematics with minimal backgrounds, but also for mathematicians which specialize in Real Analysis, Measure Theory and Functional Analysis.

MSC:
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
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