Measure Theory has played an important part in the development of functional analysis: it has been the source of many examples for functional analysis, including some which have been leading cases for major advances in the general theory, and certain results in measure theory have been applied to prove generalresults in analysis. Often the ordinary functional analyst finds the languageand a style of measure theory a stumbling block to a full understanding of these developments. Dr Fremlin’s aim in writing this book is therefore to identify those concepts in measure theory which are most relevant to functional analysis and to integrate them into functional analysis in a way consistent with that subject’s structure and habits of thought. This is achieved by approachingmeasure theory through the properties of Riesz spaces and especially topological Riesz spaces. Thus this book gathers together material which is not readily available elsewhere in a single collection and presents it in a form accessible to the first-year graduate student, whose knowledge of measure theory neednot have progressed beyond that of the ordinary lebesgue integral. INDICE: Preface; Prerequisites; 1. Riesz spaces; 2. Topological Riesz spaces; 3. Dual spaces; 4. Riesz spaces on Boolean rings; 5. Measure Algebra's; 6.Measure Spaces; 7. Representation of linear functionals; 8. Weak compactness;Appendices.
- ISBN: 978-0-521-09031-5
- Editorial: Cambridge University
- Encuadernacion: Rústica
- Páginas: 280
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés