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Author : Errol Churchill Caby
Release : 1976
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Convergence of Measures on Uniform Spaces by : Errol Churchill Caby
Download or read book Convergence of Measures on Uniform Spaces written by Errol Churchill Caby. This book was released on 1976. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir I. Bogachev
Release : 2018-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 38X/5 ( reviews)
Book Synopsis Weak Convergence of Measures by : Vladimir I. Bogachev
Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev. This book was released on 2018-09-27. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.
Author : D. Pollard
Release : 1984-10-08
Genre : Mathematics
Kind : eBook
Book Rating : 907/5 ( reviews)
Book Synopsis Convergence of Stochastic Processes by : D. Pollard
Download or read book Convergence of Stochastic Processes written by D. Pollard. This book was released on 1984-10-08. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Patrick Billingsley
Release : 2013-06-25
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)
Book Synopsis Convergence of Probability Measures by : Patrick Billingsley
Download or read book Convergence of Probability Measures written by Patrick Billingsley. This book was released on 2013-06-25. Available in PDF, EPUB and Kindle. Book excerpt: 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
Release : 2021-09-03
Genre : Education
Kind : eBook
Book Rating : 406/5 ( reviews)
Book Synopsis An Introduction to Measure Theory by : Terence Tao
Download or read book An Introduction to Measure Theory written by Terence Tao. This book was released on 2021-09-03. Available in PDF, EPUB and Kindle. Book excerpt: 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.
