Representation Theorem for Measures on Infinite Dimensional Spaces
Author : Franz Peter Edward Harpain
Publisher :
Page : 54 pages
File Size : 42,99 MB
Release : 1968
Category : Generalized spaces
ISBN :
Author : Franz Peter Edward Harpain
Publisher :
Page : 54 pages
File Size : 42,99 MB
Release : 1968
Category : Generalized spaces
ISBN :
Author : Yasuo Yamasaki
Publisher : World Scientific
Page : 276 pages
File Size : 15,93 MB
Release : 1985
Category : Science
ISBN : 9789971978525
This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.
Author : Raymond C. Fabec
Publisher : CRC Press
Page : 448 pages
File Size : 34,34 MB
Release : 2018-10-03
Category : Mathematics
ISBN : 1482285770
Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.
Author :
Publisher : Academic Press
Page : 439 pages
File Size : 22,26 MB
Release : 1972-10-16
Category : Mathematics
ISBN : 0080873634
Measure and Integration Theory on Infinite-Dimensional Spaces
Author : Charalambos D. Aliprantis
Publisher : Springer Science & Business Media
Page : 623 pages
File Size : 36,87 MB
Release : 2013-11-11
Category : Business & Economics
ISBN : 3662030047
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 math ematicians, 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.
Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 38,65 MB
Release : 2021-09-03
Category : Education
ISBN : 1470466406
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Gustave Choquet
Publisher :
Page : 384 pages
File Size : 46,71 MB
Release : 1969
Category : Calculus
ISBN :
Author : Yasuo Yamasaki
Publisher :
Page : 251 pages
File Size : 26,23 MB
Release : 1982
Category : Dimensional analysis
ISBN :
Author : Hui-Hsiung Kuo
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 29,16 MB
Release : 2003
Category : Mathematics
ISBN : 0821832026
This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross's former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross's work and permeate diverse fields. Topics include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Author : G. Kallianpur
Publisher : IMS
Page : 356 pages
File Size : 15,86 MB
Release : 1995
Category : Mathematics
ISBN : 9780940600386