Convergence of Measures on Uniform Spaces PDF Download

Author: Errol Churchill Caby
Publisher:
ISBN:
Category :
Languages : en
Pages : 122

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Author: Patrick Billingsley
Publisher: John Wiley & Sons
ISBN: 111862596X
Category : Mathematics
Languages : en
Pages : 253

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Book Description
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.

Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206

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Book Description
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: D. Pollard
Publisher: David Pollard
ISBN: 0387909907
Category : Mathematics
Languages : en
Pages : 223

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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333

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Book Description
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Author: Patrick Billingsley
Publisher: SIAM
ISBN: 9781611970623
Category : Mathematics
Languages : en
Pages : 37

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A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.

Author: Jan Pachl
Publisher: Springer Science & Business Media
ISBN: 1461450586
Category : Mathematics
Languages : en
Pages : 207

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Book Description
​This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in abstract and topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. The book is a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It presents diverse results from many sources organized in a logical whole, and includes several new results. The book is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis. The text contains a number of exercises with solution hints, and four problems with suggestions for further research.​

Author: John Roe
Publisher: American Mathematical Soc.
ISBN: 0821833324
Category : Mathematics
Languages : en
Pages : 184

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Book Description
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.

Author: Juha Heinonen
Publisher: Cambridge University Press
ISBN: 1107092345
Category : Mathematics
Languages : en
Pages : 447

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Book Description
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Author: Nancy Kress
Publisher: Macmillan
ISBN: 9780765345141
Category : Fiction
Languages : en
Pages : 372

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Book Description
Nancy Kress cemented her reputation in SF with the publication of her multiple-award–winning novella, “Beggars in Spain,” which became the basis for her extremely successful Beggars Trilogy (comprising Beggars in Spain, Beggars and Choosers, and Beggars Ride). And now she brings us Probability Space, the conclusion of the trilogy that began with Probability Moon and then Probability Sun, which is centered on the same world as Kress’s Nebula Award-winning novelette, “Flowers of Aulit Prison.” The Probability Trilogy has already been widely recognized as the next great work by this important SF writer. In Probability Space, humanity’s war with the alien Fallers continues, and it is a war we are losing. Our implacable foes ignore all attempts at communication, and they take no prisoners. Our only hope lies with an unlikely coalition: Major Lyle Kaufman, retired warrior; Marbet Grant, the Sensitive who’s involved with Kaufman; Amanda, a very confused fourteen-year-old girl; and Magdalena, one of the biggest power brokers in all of human space. As the action moves from Earth to Mars to the farthest reaches of known space, with civil unrest back home and alien war in deep space, four humans--armed with little more than an unproven theory--try to enter the Fallers’ home star system. It’s a desperate gamble, and the fate of the entire universe may hang in the balance.