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AuthorAliprantis, Charalambos D. author
TitleInfinite Dimensional Analysis [electronic resource] : A Hitchhiker's Guide / by Charalambos D. Aliprantis, Kim C. Border
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Edition Second, Completely Revised and Enlarged Edition
Connect tohttp://dx.doi.org/10.1007/978-3-662-03961-8
Descript XX, 673 p. 28 illus. online resource

SUMMARY

In the nearly five years since the publication of what we refer to as The Hitchhiker's Guide, we have been the recipients of much advice and many complaints. That, combined with the economics of the publishing industry, convinced us that the world would be a better place if we published a second edition of our book, and made it available in paperback at a more modest price. The most obvious difference between the second and the original edition is the reorganization of material that resulted in three new chapters. Chapยญ ter 4 collects many of the purely set-theoretical results about measurable structures such as semirings and a-algebras. The material in this chapter is quite independent from notions of measure and integration, and is easily acยญ cessible, so we thought it should come sooner. We also divided the chapter on correspondences into two separate chapters, one dealing with continuity, the other with measurability. The material on measurable correspondences is more detailed and, we hope, better written. We also put many of the representation theorems into their own Chapter 13. This arrangement has the side effect of forcing the renumbering of almost every result in the text, thus rendering the original version obsolete. We feel bad about that, but like Humpty Dumpty, we doubt we could put it back the way it was. The second most noticeable change is the addition of approximately seventy pages of new material


CONTENT

1 Odds and ends -- 2 Topology -- 3 Metrizable spaces -- 4 Measurability -- 5 Topological vector spaces -- 6 Normed spaces -- 7 Riesz spaces -- 8 Banach lattices -- 9 Charges and measures -- 10 Measures and topology -- 11 Integrals -- 12 Lp-spaces -- 13 Riesz Representation Theorems -- 14 Probability measures on metrizable spaces -- 15 Spaces of sequences -- 16 Correspondences -- 17 Measurable correspondences -- 18 Markov transitions -- 19 Ergodicity -- References


Mathematics Mathematical analysis Analysis (Mathematics) Functional analysis Applied mathematics Engineering mathematics Economic theory Mathematics Functional Analysis Economic Theory/Quantitative Economics/Mathematical Methods Applications of Mathematics Analysis Appl.Mathematics/Computational Methods of Engineering



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