Regular Non Additive Multimeasures Fundaments And Applications
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Regular Non Additive Multimeasures Fundaments And Applications
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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2022-10-07
Regular Non Additive Multimeasures Fundaments And Applications written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Technology & Engineering categories.
This book is intended to be an exhaustive study on regularity and other properties of continuity for different types of non-additive multimeasures and with respect to different types of topologies. The book is addressed to graduate and postgraduate students, teachers and all researchers in mathematics, but not only. Since the notions and results offered by this book are closely related to various notions of the theory of probability, this book will be useful to a wider category of readers, using multivalued analysis techniques in areas such as control theory and optimization, economic mathematics, game theory, decision theory, etc. Measure and integration theory developed during the early years of the 20th century is one of the most important contributions to modern mathematical analysis, with important applications in many fields. In the last years, many classical problems from measure theory have been treated in the non-additive case and also extended in the set-valued case. The property of regularity is involved in many results of mathematical analysis, due to its applications in probability theory, stochastic processes, optimal control problems, dynamical systems, Markov chains, potential theory etc.
Non Additive Measures
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Author : Vicenc Torra
language : en
Publisher: Springer
Release Date : 2013-10-23
Non Additive Measures written by Vicenc Torra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Technology & Engineering categories.
This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.
Atomicity Through Fractal Measure Theory
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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2019-11-02
Atomicity Through Fractal Measure Theory written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Mathematics categories.
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.
Theory Of Random Sets
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Author : Ilya Molchanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-11
Theory Of Random Sets written by Ilya Molchanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-11 with Mathematics categories.
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
50 Years With Hardy Spaces
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Author : Anton Baranov
language : en
Publisher: Birkhäuser
Release Date : 2018-03-28
50 Years With Hardy Spaces written by Anton Baranov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Mathematics categories.
Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.
Set Valued Analysis
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Author : Anca Croitoru
language : en
Publisher: Mdpi AG
Release Date : 2021-08-19
Set Valued Analysis written by Anca Croitoru and has been published by Mdpi AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.
Topologies On Closed And Closed Convex Sets
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Author : Gerald Beer
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-10-31
Topologies On Closed And Closed Convex Sets written by Gerald Beer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-31 with Mathematics categories.
This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Computational Science And Its Applications Iccsa 2018
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Author : Osvaldo Gervasi
language : en
Publisher: Springer
Release Date : 2018-07-03
Computational Science And Its Applications Iccsa 2018 written by Osvaldo Gervasi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Computers categories.
The five volume set LNCS 10960 until 10964 constitutes the refereed proceedings of the 18th International Conference on Computational Science and Its Applications, ICCSA 2018, held in Melbourne, Australia, in July 2018. Apart from the general tracks, ICCSA 2018 also includes 34 international workshops in various areas of computational sciences, ranging from computational science technologies, to specific areas of computational sciences, such as computer graphics and virtual reality. The total of 265 full papers and 10 short papers presented in the 5-volume proceedings set of ICCSA 2018, were carefully reviewed and selected from 892 submissions.
Theory Of Random Sets
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Author : Ilya Molchanov
language : en
Publisher: Springer
Release Date : 2017-12-14
Theory Of Random Sets written by Ilya Molchanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Mathematics categories.
This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.