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A Course in Analysis Volume III: Measure and Integration Theory, Complex-valued Functions of a Complex Variable by Niels Jacob, Kristian P. Evans is a nonfiction available to read on EtoBox.

What is A Course in Analysis Volume III: Measure and Integration Theory, Complex-valued Functions of a Complex Variable about?

Main subject categories: • Analysis • Measure theory • Integration theory • Complex-valued functions of a complex variableIn this third volume of "A Course in Analysis", two topics indispensible for every mathematician are treated: Measure and Integration Theory; and Complex Function Theory.In the first part measurable spaces and measure spaces are introduced and Caratheodory's extension theorem is proved. This is followed by the construction of the integral with respect to a measure, in particular with respect to the Lebesgue measure in the Euclidean space. The Radon–Nikodym theorem and the transformation theorem are discussed and much care is taken to handle convergence theorems with applications, as well as Lp-spaces.Integration on product spaces and Fubini's theorem is a further topic as is the discussion of the relation between the Lebesgue integral and the Riemann integral. In addition to these standard topics we deal with the Hausdorff measure, convolutions of functions and measures including the Friedrichs mollifier, absolutely continuous functions and functions of bounded variation. The fundamental theorem of calculus is revisited, and we also look at Sard's theorem or the

Who reads A Course in Analysis Volume III: Measure and Integration Theory, Complex-valued Functions of a Complex Variable?

Author

Niels Jacob, Kristian P. Evans

Publisher

World Scientific, World Scientific Publishing Co. Pte. Ltd.

Published

2018

Language

EN

ISBN

9789813140967

Category

nonfiction

Subjects

Mathematics, Analysis, Stem