UID:
almafu_9960119373102883
Format:
1 online resource (xiv, 266 pages) :
,
digital, PDF file(s).
ISBN:
0-511-89720-0
Content:
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 general results in analysis. Often the ordinary functional analyst finds the language and 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 approaching measure 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 need not have progressed beyond that of the ordinary lebesgue integral.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Frontmatter -- Contents -- Acknowledgements -- Preface -- Prerequisites -- Riesz spaces -- 11 Partially ordered sets -- 12 Partially ordered linear spaces -- 13 Lattices -- 14 Riesz spaces -- 15 Archimedean Riesz spaces -- 16 Linear maps between Riesz spaces -- 17 Order-dense Riesz subspaces -- 18 The countable sup property -- IX Examples for Chapter 1 -- Topological Riesz spaces -- 21 Compatible topologies -- 22 Locally solid topologies -- 23 Fatou topologies -- 24 Lebesgue topologies -- 25 Complete metrizable topologies -- 26 L-spaces and M-spaces -- 2X Examples for Chapter 2 -- Dual spaces -- 31 The space E~ -- 32 The space E× -- 33 Perfect Riesz spaces -- Riesz spaces on Boolean rings -- 41 Boolean rings -- 42 The space S(U) -- 43 The space L8(U) -- 44 The space L# -- 45 Ring homomorphisms -- 4X Examples for Chapter 4 -- Measure algebras -- 51 Measure rings -- 52 The space L1(U) -- 53 Maharam algebras -- 54 Measure-preserving ring homomorphisms -- 5X Examples for Chapter 5 -- Measure spaces -- 61 Definitions and basic properties -- 62 Measurable functions -- the space L0 -- 63 Integration -- 64 Maharam measure spaces -- 65 Banach function spaces -- 6X Examples for Chapter 6 -- Representation of linear functionals -- 71 Sequentially smooth functionals -- 72 Smooth functionals: quasi-Radon measure spaces -- 73 Radon measures and Riesz' theorem -- 7X Examples for Chapter 7 -- Weak compactness -- 81 Weak compactness in E~ -- 82 Weak compactness in E× -- 83 Weak compactness in L-spaces -- 8X Examples for Chapter 8 -- Appendix -- A1 Linear topological spaces -- A2 Spaces of continuous functions -- References -- Index of special symbols -- Index.
,
English
Additional Edition:
ISBN 0-521-09031-8
Additional Edition:
ISBN 0-521-20170-5
Language:
English
URL:
https://doi.org/10.1017/CBO9780511897207
Bookmarklink
