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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 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 Measure Integral and Probability
Author Marek Capinski
Publisher
Release 2014-09-01
Category
Total Pages 328
ISBN 9781447106463
Language English, Spanish, and French
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Book Summary:

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 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

Title Measure Integral and Probability
Author Marek Capinski
Publisher Springer Science & Business Media
Release 2013-06-29
Category Mathematics
Total Pages 227
ISBN 1447136314
Language English, Spanish, and French
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Book Summary:

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

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.

Measure Theory by Donald L. Cohn

Title Measure Theory
Author Donald L. Cohn
Publisher Springer Science & Business Media
Release 2013-07-13
Category Mathematics
Total Pages 457
ISBN 1461469562
Language English, Spanish, and French
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Book Summary:

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

Title Introdction to Measure and Probability
Author J. F. C. Kingman
Publisher Cambridge University Press
Release 2008-11-20
Category Mathematics
Total Pages
ISBN 1316582159
Language English, Spanish, and French
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Book Summary:

The authors believe that a proper treatment of probability theory requires an adequate background in the theory of finite measures in general spaces. The first part of their book sets out this material in a form that not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material (such as the various notions of convergence) which is relevant to probability theory and also the basic theory of L2-spaces, important in modern physics. The second part of the book is an account of the fundamental theoretical ideas which underlie the applications of probability in statistics and elsewhere, developed from the results obtained in the first part. A large number of examples is included; these form an essential part of the development.

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