Regular Non-Additive Multimeasures. Fundaments and Applications

This book is a comprehensive study on regularity and continuity for non-additive multimeasures and different topologies,with applications in probability theory,stochastic processes,optimal control,and more. It is intended for graduate and postgraduate students, teachers, and researchers in mathematics.

Format: Hardback
Length: 164 pages
Publication date: 08 October 2022
Publisher: Springer International Publishing AG

This comprehensive book delves into the realm of regularity and other properties of continuity for diverse non-additive multimeasures, considering various topologies. Its primary audience includes advanced graduate and postgraduate students, as well as educators and researchers across mathematics. However, its relevance extends beyond the mathematical community, as the concepts and findings presented herein have close connections to various notions of probability theory. Consequently, this book will find utility among a broader readership, particularly those utilizing multivalued analysis techniques in fields such as control theory, optimization, economic mathematics, game theory, and decision theory.

Measure and integration theory emerged in the early 20th century, playing a pivotal role in modern mathematical analysis. Over the past few years, there has been a significant resurgence of interest in treating classical problems from measure theory in the non-additive context, as well as extending these results to the set-valued setting. The concept of regularity holds immense importance in many mathematical analysis results, owing to its applications in probability theory, stochastic processes, optimal control problems, dynamical systems, Markov chains, potential theory, and more.

The book is organized into five chapters, each dedicated to exploring different aspects of regularity and continuity for non-additive multimeasures. In the first chapter, an introduction to the topic is provided, encompassing the necessary background and definitions. The subsequent chapters delve into specific topics, including the theory of regularity for non-additive measures, the convergence of non-additive integrals, and the regularity of non-additive operators. Each chapter is accompanied by a comprehensive list of exercises, designed to reinforce the understanding of the concepts discussed.

Throughout the book, numerous examples and illustrations are employed to elucidate the theoretical concepts and demonstrate their practical applications. These examples range from simple to complex, covering various fields such as probability theory, stochastic processes, optimization, and control theory. The book also includes a comprehensive bibliography, providing readers with a valuable resource for further exploration into the subject matter.

In conclusion, this book serves as an essential reference for advanced graduate and postgraduate students, educators, and researchers interested in the study of regularity and other properties of continuity for non-additive multimeasures. Its comprehensive coverage, coupled with detailed explanations and numerous examples, makes it an invaluable tool for anyone seeking to deepen their understanding of this important area of mathematics.

Weight: 430g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031110993
Edition number: 1st ed. 2023