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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 27 Nov 2023 17:39:52 +0000Positive Operators, Riesz Spaces, and Economics
https://resolver.caltech.edu/CaltechAUTHORS:20181011-142851140
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Luxemburg, Wilhelmus A. J.
Year: 1991
DOI: 10.1007/978-3-642-58199-1
Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the conference.https://authors.library.caltech.edu/records/p6hyp-bgv06Positive Operators, Riesz Spaces, and Economics
https://resolver.caltech.edu/CaltechAUTHORS:20200515-130605911
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Luxemburg, Wilhelmus A. J.
Year: 1991
DOI: 10.1007/978-3-642-58199-1
Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the confer ence.https://authors.library.caltech.edu/records/wcnfe-2bg85Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-083921808
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 1994
DOI: 10.1007/978-3-662-03004-2
This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate¬rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga¬nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit mathematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces¬sary to understand modern economic theory, but may yet prove useful in future research.https://authors.library.caltech.edu/records/wxtvp-gpj71Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-082837523
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 1999
DOI: 10.1007/978-3-662-03961-8
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. Chapter 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 accessible, 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.https://authors.library.caltech.edu/records/x9d1v-gnb48Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-082246408
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 2006
DOI: 10.1007/3-540-29587-9
This new edition of The Hitchhiker's Guide has benefitted from the comments of many individuals, which have resulted in the addition of some new material, and the reorganization of some of the rest. The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions. There is much more material on the special properties of convex sets and functions in finite dimensional spaces. There are improvements and additions in almost every chapter. There is more new material than might seem at first glance, thanks to a change in font that reduced the page count about five percent. We owe a huge debt to Valentina Galvani, Daniela Puzzello, and Francesco Rusticci, who were participants in a graduate seminar at Purdue University and whose suggestions led to many improvements, especially in chapters five through eight. We particularly thank Daniela Puzzello for catching uncountably many errors throughout the second edition, and simplifying the statements of several theorems and proofs. In another graduate seminar at Caltech, many improvements and corrections were suggested by Joel Grus, PJ Healy, Kevin Roust, Maggie Penn, and Bryan Rogers.https://authors.library.caltech.edu/records/jj552-gpj20