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Field name	Details
Dewey Class	515
Title	Integration and Modern Analysis ([Ebook]) / by John J. Benedetto, Wojciech Czaja.
Author	Benedetto, John J. , 1939-
Added Personal Name	Czaja, Wojciech
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2009.
Physical Details	XIX, 575 pages:. 24 illus. : online resource.
Series	Birkhäuser Advanced Texts / Basler Lehrbücher
ISBN	9780817646561
Summary Note	A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the DieudonnÃ©âGrothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinating historical commentary interwoven into the exposition; * Hundreds of problems from routine to challenging; * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; * Two significant appendices on functional analysis and Fourier analysis. Key Topics: * In-depth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; * Evolution of the Riesz representation theorem to Radon measures and distribution theory; * Deep results in modern differentiation theory; * Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and HahnâSaks; * Thorough treatment of rearrangements and maximal functions; * The relation between surface measure and Hausforff measure; * Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.:
Contents note	Preface -- Classical real variables -- Lebesgue measure and general measure theory -- The Lebesgue integral -- The relationship between differentiation and integration on R -- Spaces of measures and the RadonâNikodym theorem -- Weak convergence of measures -- Riesz representation theorem -- Lebesgue differentiation theorem on Rd -- Self-similar sets and fractals -- Appendix I: Functional analysis -- Appendix II: Fourier Analysis -- References -- Index.
System details note	Online Access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4656-1
Links to Related Works	Subject References: Analysis . Functions of a Complex Variable . Functions of complex variables . Global analysis (Mathematics) . Mathematics . Measure and Integration . Authors: author . Benedetto, John J. 1939- . Czaja, Wojciech . Corporate Authors: SpringerLink (Online service) . Series: Birkhäuser Advanced Texts / Basler Lehrbücher . Classification: 515 . 515 (DDC 23) .

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Integration and Modern Analysis

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