Probabilistic Metric Spaces

Probabilistic Metric Spaces PDF

Author: B. Schweizer

Publisher: Courier Corporation

Published: 2011-10-14

Total Pages: 354

ISBN-13: 0486143759

DOWNLOAD EBOOK →

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.

Probability Measures on Metric Spaces

Probability Measures on Metric Spaces PDF

Author: K. R. Parthasarathy

Publisher: Academic Press

Published: 2014-07-03

Total Pages: 289

ISBN-13: 1483225259

DOWNLOAD EBOOK →

Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.

Fixed Point Theory in Probabilistic Metric Spaces

Fixed Point Theory in Probabilistic Metric Spaces PDF

Author: O. Hadzic

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 279

ISBN-13: 9401715602

DOWNLOAD EBOOK →

Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.

Nonlinear Operator Theory in Probablistic Metric Spaces

Nonlinear Operator Theory in Probablistic Metric Spaces PDF

Author: Shih-sen Chang

Publisher: Nova Publishers

Published: 2001

Total Pages: 358

ISBN-13: 9781560729808

DOWNLOAD EBOOK →

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.

Gradient Flows

Gradient Flows PDF

Author: Luigi Ambrosio

Publisher: Springer Science & Business Media

Published: 2005-01-28

Total Pages: 348

ISBN-13: 9783764324285

DOWNLOAD EBOOK →

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.

Gradient Flows

Gradient Flows PDF

Author: Luigi Ambrosio

Publisher: Springer Science & Business Media

Published: 2008-10-29

Total Pages: 334

ISBN-13: 376438722X

DOWNLOAD EBOOK →

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.

Triangular Norms

Triangular Norms PDF

Author: Erich Peter Klement

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 391

ISBN-13: 9401595402

DOWNLOAD EBOOK →

This book discusses the theory of triangular norms and surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals. It includes many graphical illustrations and gives a well-balanced picture of theory and applications. It is for mathematicians, computer scientists, applied computer scientists and engineers.

On Nonsymmetric Topological and Probabilistic Structures

On Nonsymmetric Topological and Probabilistic Structures PDF

Author: Yeol Je Cho

Publisher: Nova Publishers

Published: 2006

Total Pages: 230

ISBN-13: 9781594549175

DOWNLOAD EBOOK →

In this book, generally speaking, some properties of bitopological spaces generated by certain non-symmetric functions are studied. These functions, called "probabilistic quasi-pseudo-metrics" and "fuzzy quasi-pseudo-metrics", are generalisations of classical quasi-pseudo metrics. For the sake of completeness as well as for convenience and easy comparison, most of the introductory paragraphs are mainly devoted to fundamental notions and results from the classical -- deterministic or symmetric -- theory.

Lanterna Rally - Theme by Grace Themes