{"product_id":"measure-and-integral","title":"Measure and Integral","description":"\u003cp\u003eNow considered a classic text on the topic,\u003cb\u003e Measure and Integral: An Introduction to Real Analysis\u003c\/b\u003e provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.\u003c\/p\u003e\u003cp\u003ePublished nearly forty years after the first edition, this long-awaited \u003cb\u003eSecond Edition \u003c\/b\u003ealso:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eStudies the Fourier transform of functions in the spaces \u003ci\u003eL1\u003c\/i\u003e, \u003ci\u003eL2\u003c\/i\u003e, and \u003ci\u003eLp\u003c\/i\u003e, 1 \u0026lt; \u003ci\u003ep\u003c\/i\u003e \u0026lt; 2\u003c\/li\u003e\n\u003cli\u003eShows the Hilbert transform to be a bounded operator on \u003ci\u003eL2\u003c\/i\u003e, as an application of the \u003ci\u003eL2\u003c\/i\u003e theory of the Fourier transform in the one-dimensional case\u003c\/li\u003e\n\u003cli\u003eCovers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation\u003c\/li\u003e\n\u003cli\u003eDerives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension\u003c\/li\u003e\n\u003cli\u003eExtends the subrepresentation formula derived for smooth functions to functions with a weak gradient\u003c\/li\u003e\n\u003cli\u003eApplies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases\u003c\/li\u003e\n\u003cli\u003eProves the existence of a tangent plane to the graph of a Lipschitz function of several variables\u003c\/li\u003e\n\u003cli\u003eIncludes many new exercises not present in the first edition\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThis widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":54234647134552,"sku":"9781498702898","price":137.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9781498702898_7eadc208-3776-4730-9da5-b4eb2d377bab.jpg?v=1777257017","url":"https:\/\/agendabookshop.com\/products\/measure-and-integral","provider":"Agenda Bookshop","version":"1.0","type":"link"}