## measure,integral,derivative - Universitext Sergei...

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Preview this item Preview this item. Series: Universitext. With over exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis.

In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students.

With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where [sigma]-algebras are not used in the text on measure theory and Dini's derivatives are not used in the chapter on differentiation.

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However, all the main results of Lebesgue's theory are found in the book. Read more Show all links.

Allow this favorite library to be seen by others Keep this favorite library private. Find a copy in the library Finding libraries that hold this item Featuring over exercises, this text for a one-semester course in Lebesgue's theory takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. Reviews Editorial reviews. Publisher Synopsis From the reviews:"It is accessible to upper-undergraduate and lower graduate level students, and the only prerequisite is a course in elementary real analysis.

User-contributed reviews Add a review and share your thoughts with other readers. Be the first. Add a review and share your thoughts with other readers. Similar Items Related Subjects: 12 Lebesgue integral. Measure and Integration. Real Functions. Global analysis Mathematics. Linked Data More info about Linked Data. All rights reserved. Privacy Policy Terms and Conditions. Remember me on this computer. Cancel Forgot your password?

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This classroom-tested text is intended for a one-semester course in Lebesgue's theory. Lebesgue integral. Similar Items. Table of contents Contributor biographical information Publisher description. Armonic functions Contour integrals. Cauchy's Theorem. Cauchy's integral formula.

## Measure, integral, derivative - CERN Document Server

Maximum modulus theorem. Liouville's theorem. Morera theorem. Series representation of analytic functions. Taylor's theorem. Laurent's series and classification of singularities Calculus of residues. The residue theorem. Application in evaluation of integrals on the real line and Principal Value.

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The logarithmic residue, Rouche's theorem. Plancherel theorem.

## Measure, Integral, Derivative

Laplace transform and applications. Improve unconventional thinking. Marsden, M.

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Hoffman, Basic complex analysis. Freeman New York. Rudin, Real and complex analysis. Mc Graw Hill. Module Functional analysis Terence Tao, An introduction to measure theory. Haim Brezis, Functional analysis, Sobolev spaces and partial differential equations.

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- measure,integral,derivative - Universitext Sergei....

Springer, New York,. With applications to linear partial different. Graduate Studies in Mathematics, Michael Reed, Barry Simon, Methods of modern mathematical physics.