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Title Measure Integral and Probability
Author Marek Capinski
Publisher Springer Science & Business Media
Release 2013-12-01
Category Mathematics
Total Pages 311
ISBN 1447106458
Language English, Spanish, and French
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Book Summary:

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Title Measure Integral and Probability
Author Marek Capinski
Publisher
Release 2014-01-15
Category
Total Pages 240
ISBN 9781447136323
Language English, Spanish, and French
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Book Summary:

Title Measure Theory and Probability
Author Malcolm Adams
Publisher Springer Science & Business Media
Release 2013-04-17
Category Mathematics
Total Pages 206
ISBN 1461207797
Language English, Spanish, and French
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Book Summary:

"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association

Measure and Integral by Konrad Jacobs

Title Measure and Integral
Author Konrad Jacobs
Publisher Academic Press
Release 2014-07-10
Category Mathematics
Total Pages 592
ISBN 1483263045
Language English, Spanish, and French
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Book Summary:

Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

Title Integral Probability and Fractal Measures
Author Gerald A. Edgar
Publisher Springer Science & Business Media
Release 2013-03-14
Category Mathematics
Total Pages 286
ISBN 1475729588
Language English, Spanish, and French
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Book Summary:

Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.

Title Measure Integral Probability Processes
Author René L Schilling
Publisher
Release 2021-02-02
Category
Total Pages 450
ISBN
Language English, Spanish, and French
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Book Summary:

In these lecture notes we give a self-contained and concise introduction to the essentials of modern probability theory. The material covers all concepts and techniques usually taught at BSc and first-year graduate level probability courses: Measure & integration theory, elementary probability theory, further probability, classic limit theorems, discrete-time and continuous-time martingales, Poisson processes, random walks & Markov chains and, finally, first steps towards Brownian motion. The text can serve as a course companion, for self study or as a reference text. Concepts, which will be useful for later chapters and further studies are introduced early on. The material is organized and presented in a way that will enable the readers to continue their study with any advanced text in probability theory, stochastic processes or stochastic analysis. Much emphasis is put on being reader-friendly and useful, giving a direct and quick start into a fascinating mathematical topic.

Title Measures Integrals and Martingales
Author Ren L. Schilling
Publisher Cambridge University Press
Release 2017-04-03
Category Mathematics
Total Pages 490
ISBN 1316620247
Language English, Spanish, and French
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Book Summary:

A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.

Title Measure Integration and Probability
Author Claude W. Burrill
Publisher
Release 1972
Category Integrals, Generalized
Total Pages 464
ISBN
Language English, Spanish, and French
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Book Summary:

Metric spaces; Functions on metric spaces; Fields; Measure; Integration; Differentiation; Types of convergence; Hilbert space; Probability; Characteristic functions; Almost sure convergence; Central limit problem; Conditional probability, conditional expectation and martingales; Stochastic processes.

Title MEASURE THEORY AND PROBABILITY
Author A. K. BASU
Publisher PHI Learning Pvt. Ltd.
Release 2012-04-21
Category Mathematics
Total Pages 240
ISBN 8120343859
Language English, Spanish, and French
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Book Summary:

This compact and well-received book, now in its second edition, is a skilful combination of measure theory and probability. For, in contrast to many books where probability theory is usually developed after a thorough exposure to the theory and techniques of measure and integration, this text develops the Lebesgue theory of measure and integration, using probability theory as the motivating force. What distinguishes the text is the illustration of all theorems by examples and applications. A section on Stieltjes integration assists the student in understanding the later text better. For easy understanding and presentation, this edition has split some long chapters into smaller ones. For example, old Chapter 3 has been split into Chapters 3 and 9, and old Chapter 11 has been split into Chapters 11, 12 and 13. The book is intended for the first-year postgraduate students for their courses in Statistics and Mathematics (pure and applied), computer science, and electrical and industrial engineering. KEY FEATURES : Measure theory and probability are well integrated. Exercises are given at the end of each chapter, with solutions provided separately. A section is devoted to large sample theory of statistics, and another to large deviation theory (in the Appendix).

Generalized Measure Theory by Zhenyuan Wang

Title Generalized Measure Theory
Author Zhenyuan Wang
Publisher Springer Science & Business Media
Release 2010-07-07
Category Mathematics
Total Pages 384
ISBN 0387768521
Language English, Spanish, and French
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Book Summary:

Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

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