{"product_id":"integration-and-modern-analysis-9780817643065","title":"Integration and Modern Analysis","description":"\u003cp\u003e • Author(s): John J. Benedetto\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eA 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 Dieudonné-Grothendieck theorem and other intricate developments dealing with weak convergence of measures.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eKey Features: \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e* Fascinating historical commentary interwoven into the exposition;\u003c\/p\u003e\u003cp\u003e* Hundreds of problems from routine to challenging;\u003c\/p\u003e\u003cp\u003e* Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects;\u003c\/p\u003e\u003cp\u003e* Two significant appendices on functional analysis and Fourier analysis.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eKey Topics: \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e* In-depth development of measure theory and Lebesgue integration;\u003c\/p\u003e\u003cp\u003e* Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results;\u003c\/p\u003e\u003cp\u003e* Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals;\u003c\/p\u003e\u003cp\u003e* Evolution of the Riesz representation theorem to Radon measures and distribution theory;\u003c\/p\u003e\u003cp\u003e* Deep results in modern differentiation theory;\u003c\/p\u003e\u003cp\u003e* Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn-Saks;\u003c\/p\u003e\u003cp\u003e* Thorough treatment of rearrangements and maximal functions;\u003c\/p\u003e\u003cp\u003e* The relation between surface measure and Hausforff measure;\u003c\/p\u003e\u003cp\u003e* Complete presentation of Besicovich coverings and differentiation of measures.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntegration and Modern Analysis\u003c\/i\u003e will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45274179109015,"sku":"9780817643065","price":9447.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780817643065.webp?v=1769279126","url":"https:\/\/atlanticbooks.com\/products\/integration-and-modern-analysis-9780817643065","provider":"Atlantic Books","version":"1.0","type":"link"}