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(?;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(?;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.
| ISBN: | 9781786300133 |
| Publication date: | 19th January 2026 |
| Author: | Jacques Simon |
| Publisher: | Wiley-ISTE an imprint of Wiley |
| Format: | Hardback |
| Pagination: | 448 pages |
| Genres: |
Mathematics |
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(?;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(?;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.
Integration features in the following genres: Mathematics
Integration is available in Hardback
Integration was written by Jacques Simon and published by Wiley-ISTE an imprint of Wiley
Integration has 448 pages
£111.60