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Integration
Hardcover
ISBN13: 9781786300133
Publisher: Wiley-Iste
Published: Jun 10 2019
Pages: 448
Weight: 1.77
Height: 1.00 Width: 6.14 Depth: 9.21
Language: English
This 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.
We 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.
Integration 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.
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