{"product_id":"integration-jacques-simon-9781786300133","title":"Integration","description":"\u003cp\u003eThis book presents a simple and novel theory of integration, both real and vectorial, particularly suitable for the study of PDEs. This theory allows for integration with values in a Neumann space E, i.e. in which all Cauchy sequences converge, encompassing Neumann and Fréchet spaces, as well as \"weak\" spaces and distribution spaces.\u003c\/p\u003e \u003cp\u003eWe integrate \"integrable measures\", which are equivalent to \"classes of integrable functions which are a.e. equals\" when E is a Fréchet space. More precisely, we associate the measure f with a class f, where f(u) is the integral of fu for any test function u. The classic space Lp(Ω;E) is the set of f, and ours is the set of f; these two spaces are isomorphic.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntegration\u003c\/i\u003e studies, in detail, for any Neumann space E, the properties of the integral and of Lp(Ω;E): regularization, image by a linear or multilinear application, change of variable, separation of multiple variables, compacts and duals. When E is a Fréchet space, we study the equivalence of the two definitions and the properties related to dominated convergence.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Jacques Simon\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1786300133\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781786300133\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Wiley-Iste\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/10\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 448\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.77lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.00d","brand":"Jacques Simon","offers":[{"title":"Hardcover","offer_id":48453919244543,"sku":"9781786300133","price":165.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_69a0aa44-04db-4c7b-b8be-7f9523885ebc.jpg?v=1777303029","url":"https:\/\/www.whiterainbookhouse.com\/products\/integration-jacques-simon-9781786300133","provider":"WR Book House","version":"1.0","type":"link"}