Lectures on Probabilistic Metric Spaces
Author | : Berthold Schweizer |
Publisher | : |
Total Pages | : 150 |
Release | : 1965 |
Genre | : Topology |
ISBN | : |
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Author | : Berthold Schweizer |
Publisher | : |
Total Pages | : 150 |
Release | : 1965 |
Genre | : Topology |
ISBN | : |
Author | : B. Schweizer |
Publisher | : Courier Corporation |
Total Pages | : 354 |
Release | : 2011-10-14 |
Genre | : Mathematics |
ISBN | : 0486143759 |
This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
Author | : Luigi Ambrosio |
Publisher | : Springer Science & Business Media |
Total Pages | : 333 |
Release | : 2008-10-29 |
Genre | : Mathematics |
ISBN | : 376438722X |
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 | : Joel Spencer |
Publisher | : SIAM |
Total Pages | : 98 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9781611970074 |
This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties.
Author | : B. Schweizer |
Publisher | : Courier Corporation |
Total Pages | : 354 |
Release | : 2011-11-30 |
Genre | : Mathematics |
ISBN | : 0486445143 |
This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1976 |
Genre | : |
ISBN | : |
Author | : Luigi Ambrosio |
Publisher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2006-03-30 |
Genre | : Mathematics |
ISBN | : 3764373091 |
This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.
Author | : Wendelin Werner |
Publisher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : |
Genre | : |
ISBN | : 9783540213161 |
Author | : Diego Bricio Hern ndez |
Publisher | : World Scientific |
Total Pages | : 172 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9789810219086 |
This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered.The book is a valuable guide for higher level engineering students.
Author | : Shih-sen Chang |
Publisher | : Nova Publishers |
Total Pages | : 358 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9781560729808 |
The purpose of this book is to give a comprehensive introduction to the study of non-linear operator theory in probabilistic metric spaces. This book is introduced as a survey of the latest and new results on the following topics: Basic theory of probabilistic metric spaces; Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces; Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces; Coincidence point theorems, minimisation and fixed degree theorems in probabilistic metric spaces; Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces; Nonlinear semigroups and differential equations in probabilistic metric spaces; KKM theorems, minimax theorems and variational inequalities.