{"product_id":"measure-and-integral-9781498702898","title":"Measure and Integral","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\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 \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 \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 \u003cli\u003eCovers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation\u003c\/li\u003e \u003cl\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreliminaries. Functions of Bounded Variation and the Riemann–Stieltjes Integral. Lebesgue Measure and Outer Measure. Lebesgue Measurable Functions. The Lebesgue Integral. Repeated Integration. Differentiation. \u003ci\u003eLp\u003c\/i\u003e Classes. Approximations of the Identity and Maximal Functions. Abstract Integration. Outer Measure and Measure. A Few Facts from Harmonic Analysis. The Fourier Transform. Fractional Integration. Weak Derivatives and Poincaré–Sobolev Estimates.\u003c\/p\u003e\u003c\/l\u003e\n\u003c\/ul\u003e","brand":"CRC Press","offers":[{"title":"Default Title","offer_id":51019953930583,"sku":"9781498702898","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498702898.jpg?v=1750781864","url":"https:\/\/bookcurl.com\/products\/measure-and-integral-9781498702898","provider":"Book Curl","version":"1.0","type":"link"}