Download or read book Integration of Set valued Functions written by Pieter Maritz and published by . This book was released on 1975 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Integral of Set valued Functions written by Zvi Artstein and published by . This book was released on 1973 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Valued Stochastic Integrals and Applications written by Michał Kisielewicz and published by Springer Nature. This book was released on 2020-06-26 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued Itô , set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings. The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.
Download or read book Approximation Of Set valued Functions Adaptation Of Classical Approximation Operators written by Nira Dyn and published by World Scientific. This book was released on 2014-10-30 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
Download or read book Integration of set valued functions written by Pieter Maritz and published by . This book was released on 1975 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Valued Analysis written by Jean-Pierre Aubin and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. ...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "This book provides a thorough introduction to multivalued or set-valued analysis... The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math
Download or read book Limit Theorems and Applications of Set Valued and Fuzzy Set Valued Random Variables written by Shoumei Li and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.
Download or read book Integral of Real set valued Set Functions with Respect to Banach set valued Measures written by Leben Li Wee and published by . This book was released on 1969 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Valued Measures and Integrals for Cone Valued Functions written by Walter Roth and published by Springer Science & Business Media. This book was released on 2009-02-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.
Download or read book Unification and Set Valued Functions for Functional and Logic Programming written by Frank S. Silbermann and published by . This book was released on 1987 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors propose a new approach to the integration of functional and logic languages, based on a theory of unification and set valued functions. A set-valued function maps a tuple of input sets into an output set. This document a language called Setlog illustrates this approach, and gives its model-theoretic, fixed-point, and operational semantics. The model-theoretic semantics and fixed-point semantics resemble that of Horn logic. The operational semantics uses outermost reduction (for set-valued functions) and unification (for terms). The correctness of the operational semantics is established through soundness and completeness proofs. Keywords: Syntax; Set theory.
Download or read book Integral Representation written by Walter Roth and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-10-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.
Download or read book Soft Methods for Handling Variability and Imprecision written by Didier Dubois and published by Springer Science & Business Media. This book was released on 2008-10-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.
Download or read book Measure and Integration written by Hari Bercovici and published by Springer. This book was released on 2016-03-17 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems.
Download or read book Approximation of Set valued Functions written by Nira Dyn and published by . This book was released on 2014 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
Download or read book Atomicity through Fractal Measure Theory written by Alina Gavriluţ and published by Springer Nature. This book was released on 2019-11-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.
Download or read book Space Structure and Randomness written by Michel Bilodeau and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.
Download or read book Stochastic and Integral Geometry written by R.V. Ambartzumian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
