00000cmm a22000004a 4500 UP-99796217611212289 Buklod 20250130112614.0 m go j cr |nu|||auu|a 250130s2011 nyu o j eng d 9781461411352 (eBook) 1461411351 (eBook) (iLib)UPD-00215704046 DMLR rda. eng DMLUC QA 312 S783 2011eb Stroock, Daniel W. author. Essentials of integration theory for analysis [electronic resource] Daniel W. Stroock. Integration theory for analysis. New York, New York Springer New York 2011. 1 online resource (xi, 243 pages) text rdacontent computer rdamedia online resource rdacarrier Graduate texts in mathematics 262. "A substantial revision of ... [the author's] A concise introduction to the theory of integration ... appropriate as a text for a one-semester graduate course in integration theory"--Back cover. The classical theory -- Measures -- Lebesgue integration -- Products of measures -- Changes of variable -- Basic inequalities and Legesgue spaces -- Hilbert space and elements of Fourier analysis -- The Radon-Nikodym theorem, Daniell integration, and Carathâeodory's extension theorem. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhäuser title by the same author,  A Concise Introduction to the Theory of Integration. Highlights of this new textbook for the GTM series include revisions to Chapter 1 which add a section about the rate of convergence of Riemann sums and introduces a discussion of the Euler?MacLauren formula.  In Chapter 2, where Lebesque?s theory is introduced, a construction of the countably additive measure is done with sufficient generality to cover both Lebesque and Bernoulli  measures. Chapter 3 includes a proof of Lebesque?s differential theorem for all monotone functions and the concluding chapter has been expanded to include a proof of Carathéory?s  method for constructing measures and his result is applied to the construction of the Hausdorff measures. This new gem is appropriate as a text for a one-semester graduate course in integration theory and is complimented by the addition of several problems related to the new material.  The text is also highly useful for self-study. A complete solutions manual is available for instructors who adopt the text for their courses. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Integrals, Generalized. Measure theory. Fourier analysis. Integration, Functional. Mathematical analysis. SpringerLink (Online service). Electronic Resource Available for UP System via SpringerLink. https://doi.org/10.1007/978-1-4614-1135-2 FO UPD DMLR QA 312 S783 2011eb Electronic Resource