Titlebook: Introduction to Measure Theory and Integration; Luigi Ambrosio,Giuseppe Prato,Andrea Mennucci Textbook 2011 Scuola Normale Superiore Pisa

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The fundamental theorem of the integral calculus,ance, typically one requires the continuity of .). We will see that this gap basically disappears in Le-besgue’ theory, and that there is a precise characterization of the class of functions representable as . ∫. g(.) . for a suitable (Lebesgue) integrable function . and for some constant

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Fourier series,ow that many different choices are indeed possible). Thanks to the theory of . spaces and of Hilbert spaces developed in the previous chapters, the problem can be formalized by looking for complete orthonormal systems in . made by trigonometric functions.

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