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28Axx Measure and integration -- Classical measure theory

42A16 Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series En-ligne: Springerlink | Zentralblatt | MathSciNet

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This carefully prepared textbook from Springer’s Universitext series devotes to a modern version of classical calculus. The authors base the standard theory of integration and differentiation on a more general (in fact, more simple) approach of measure theory. The presented exposition allows to more easily integrate calculus into modern analysis and it includes several attractive applications (Brun-Minkowski and Brower theorems, Khintchine and K. Ball inequalities etc.). The text is accompanied by a lot of examples and exercises. (Zentralblatt)

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