Measure, Integral and Probability

by Marek Capinski

Author	: Marek Capinski
Publisher	: Springer Science & Business Media
Total Pages	: 229
Release	: 2013-06-29
Genre	: Mathematics
ISBN	: 1447136314

GET BOOK

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, Integral, Probability & Processes

by René L Schilling

Author	: René L Schilling
Publisher	:
Total Pages	: 450
Release	: 2021-02-02
Genre	:
ISBN	:

GET BOOK

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.

Integration, Measure and Probability

by H. R. Pitt

Author	: H. R. Pitt
Publisher	: Courier Corporation
Total Pages	: 130
Release	: 2012-01-01
Genre	: Mathematics
ISBN	: 0486488152

GET BOOK

Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

Measures, Integrals and Martingales

by René L. Schilling

Author	: René L. Schilling
Publisher	: Cambridge University Press
Total Pages	: 404
Release	: 2005-11-10
Genre	: Mathematics
ISBN	: 9780521850155

GET BOOK

This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.

Measure, Integration and a Primer on Probability Theory

by Stefano Gentili

Author	: Stefano Gentili
Publisher	: Springer Nature
Total Pages	: 458
Release	: 2020-11-30
Genre	: Mathematics
ISBN	: 3030549402

GET BOOK

The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject from a wider angle, thus appreciating the human side of major figures in Mathematics. The style in which topics are addressed, albeit informal, always maintains a rigorous character. The attention placed in the careful layout of the logical steps of proofs, the abundant examples and the supplementary remarks disseminated throughout all contribute to render the reading pleasant and facilitate the learning process. The exposition is particularly suitable for students of Mathematics, Physics, Engineering and Statistics, besides providing the foundation essential for the study of Probability Theory and many branches of Applied Mathematics, including the Analysis of Financial Markets and other areas of Financial Engineering.

Probability and Measure

by Patrick Billingsley

Author	: Patrick Billingsley
Publisher	: John Wiley & Sons
Total Pages	: 612
Release	: 2017
Genre	:
ISBN	: 9788126517718

GET BOOK

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

Counterexamples in Measure and Integration

by René L. Schilling

Author	: René L. Schilling
Publisher	: Cambridge University Press
Total Pages	: 431
Release	: 2021-06-17
Genre	: Mathematics
ISBN	: 1009020390

GET BOOK

Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).

Introduction to Measure Theory and Integration

by Luigi Ambrosio

Author	: Luigi Ambrosio
Publisher	: Springer Science & Business Media
Total Pages	: 193
Release	: 2012-02-21
Genre	: Mathematics
ISBN	: 8876423869

GET BOOK

This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.

Integration and Probability

by Paul Malliavin

Author	: Paul Malliavin
Publisher	: Springer Science & Business Media
Total Pages	: 341
Release	: 2012-12-06
Genre	: Mathematics
ISBN	: 1461242029

GET BOOK

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.