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Book Summary
Integration is one of the two cornerstones of analysis. Since the fundamental
work of Lebesgue, integration has been presented in terms of measure theory.
This introductory text starts with the historical development of the notion of
the integral and a review of the Riemann integral. From here, the reader is
naturally led to the consideration of the Lebesgue integral, where abstract
integration is developed via measure theory. The important basic topics are all
covered: the Fundamental Theorem of Calculus, Fubini?s Theorem, Lp spaces, the
Radon-Nikodym Theorem, change of variables formulas, and so on.The text is
written in an informal style to make the subject matter easily
Integration is one of the two cornerstones of analysis. Since the fundamental
work of Lebesgue, integration has been presented in terms of measure theory.
This introductory text starts with the historical development of the notion of
the integral and a review of the Riemann integral. From here, the reader is
naturally led to the consideration of the Lebesgue integral, where abstract
integration is developed via measure theory. The important basic topics are all
covered: the Fundamental Theorem of Calculus, Fubini?s Theorem, Lp spaces, the
Radon-Nikodym Theorem, change of variables formulas, and so on.The text is
written in an informal style to make the subject matter easily