Ideal spaces are a very general class of normed spaces of measurable functions, which includes e.g. Lebesgue and Orlicz spaces. Their most important application is in functional analysis in the theory of (usual and partial) integral and integro-differential equations. The book is a rather complete and self-contained introduction into the general theory of ideal spaces. Some emphasis is put on spaces of vector-valued functions and on the constructive viewpoint of the theory (without the axiom of choice). The reader should have basic knowledge in functional analysis and measure theory.
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978-3-540-69192-1 (9783540691921)
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Schweitzer Klassifikation
Introduction.- Basic definitions and properties.- Ideal spaces with additional properties.- Ideal spaces on product measures and calculus.- Operators and applications.- Appendix: Some measurability results.- Sup-measurable operator functions.- Majorising principles for measurable operator functions.- A generalization of a theorem of Luxemburg-Gribanov.- References.- Index.
