The Riemann Approach To Integration

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The Riemann Approach To Integration

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Author : Washek F. Pfeffer
language : en
Publisher: Cambridge University Press
Release Date : 1993

The Riemann Approach To Integration written by Washek F. Pfeffer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

A detailed exposition of generalised Riemann-Stieltjes integrals.

Riemann S Method Of Integration

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Author : E. W. Montroll
language : en
Publisher:
Release Date : 1952

Riemann S Method Of Integration written by E. W. Montroll and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Compressors categories.

Integration A Functional Approach

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Author : Klaus Bichteler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23

Integration A Functional Approach written by Klaus Bichteler 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 2010-11-23 with Mathematics categories.

This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.

Lebesgue S Theory Of Integration

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Author : Rahul Jain
language : en
Publisher: Springer Nature
Release Date : 2025-06-11

Lebesgue S Theory Of Integration written by Rahul Jain and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-11 with Mathematics categories.

This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration. Translated into English for the first time, the book offers readers a unique opportunity to explore Lebesgue’s groundbreaking ideas and delves into the mind of one of the greatest mathematicians in history. The book provides historical context and explanations that enhance readers’ comprehension and appreciation of the material. Covering a wide range of topics, from the integration before Riemann to the search for primitive functions, it offers a comprehensive understanding of Lebesgue’s theories and their significance in the field of mathematics. It inspires readers to explore further in the field, stimulates new ideas, and opens avenues for future research. The book bridges the gap between theory and practice by providing examples and applications that contributed to the development of Lebesgue integration theory. The book serves as a valuable resource for courses in analysis, measure theory, and Lebesgue integration theory, providing students with the opportunity to study the original work of Lebesgue and deepen their understanding of integration theory. It is meant for a broad audience, including advanced undergraduate and graduate students, mathematics scholars, researchers, educators, and enthusiasts, seeking a comprehensive understanding of Lebesgue’s theories and the historical development of integration theory. Mathematicians and researchers will find this book essential for its historical significance and the preservation of important mathematical literature.

A Ramble Through Probability

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Author : Samopriya Basu
language : en
Publisher: SIAM
Release Date : 2024-03-06

A Ramble Through Probability written by Samopriya Basu and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-06 with Mathematics categories.

Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website. This book is intended for graduate students in engineering, mathematics, science, and statistics. Researchers who need to use probability theory will also find it useful. It is appropriate for graduate-level courses on measure theory and/or probability theory.

Gauge Integral Structures For Stochastic Calculus And Quantum Electrodynamics

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Author : Patrick Muldowney
language : en
Publisher: John Wiley & Sons
Release Date : 2021-04-23

Gauge Integral Structures For Stochastic Calculus And Quantum Electrodynamics written by Patrick Muldowney and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.

GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics. Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author’s previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable. Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics takes a gradual, relaxed, and discursive approach to the subject in a successful attempt to engage the reader by exploring a narrower range of themes and problems. Organized around examples with accompanying introductions and explanations, the book covers topics such as: Stochastic calculus, including discussions of random variation, integration and probability, and stochastic processes Field theory, including discussions of gauges for product spaces and quantum electrodynamics Robust and thorough appendices, examples, illustrations, and introductions for each of the concepts discussed within An introduction to basic gauge integral theory (for those unfamiliar with the author’s previous book) The methods employed in this book show, for instance, that it is no longer necessary to resort to unreliable “Black Box” theory in financial calculus; that full mathematical rigor can now be combined with clarity and simplicity. Perfect for students and academics with even a passing interest in the application of the gauge integral technique pioneered by R. Henstock and J. Kurzweil, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics is an illuminating and insightful exploration of the complex mathematical topics contained within.

Selected Topics On Generalized Integration

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Author : Tin Lam Toh
language : en
Publisher: World Scientific
Release Date : 2025-05-20

Selected Topics On Generalized Integration written by Tin Lam Toh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Mathematics categories.

This comprehensive volume offers an in-depth exploration of advanced integration theories, extending beyond classical methods to unify and expand the field. Building on the foundational work of Jaroslav Kurzweil and Ralph Henstock, the book delves into the Henstock-Kurzweil and McShane gauge integrals, presenting a more intuitive and versatile alternative to the traditional Lebesgue integral. By bridging gaps in existing literature, the authors provide a rigorous treatment of integration on metric measure spaces, exploring critical concepts such as completeness, compactness, and Cousin's lemma.The book systematically introduces advanced topics, including the variational Henstock integral in locally convex spaces, the Riemann-Lebesgue integral for vector-valued functions, and generalizations of the Sugeno integral. Further chapters explore convergence in Banach spaces on time scales, set-valued integrals, and applications to harmonic analysis and partial differential equations, including solutions to the heat equation in distribution spaces.Notably, the text presents innovative approaches like the symmetric Laplace integral and the q-Homotopy Analysis Method for solving nonlinear integral equations, offering practical tools for modern analysis. Unified integral representations for generalized Mittag-Leffler functions further highlight the book's engagement with special functions.Ideal for researchers and advanced students in mathematical analysis, this book seamlessly integrates classical theories with modern advancements, offering both theoretical insights and practical applications across mathematics, physics, and engineering.

The Integrals Of Lebesgue Denjoy Perron And Henstock

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Author : Russell A. Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

The Integrals Of Lebesgue Denjoy Perron And Henstock written by Russell A. Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

Offers an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. This book contains over 230 exercises (with solutions) that illustrate and expand the material. It is suitable for first-year graduate students who have background in real analysis.

From The Calculus To Set Theory 1630 1910

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Author : Ivor Grattan-Guinness
language : en
Publisher: Princeton University Press
Release Date : 2020-10-06

From The Calculus To Set Theory 1630 1910 written by Ivor Grattan-Guinness and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.

From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Møller-Pedersen.

Foundations Of Quantitative Finance Book Iii The Integrals Of Riemann Lebesgue And Riemann Stieltjes

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Author : Robert R. Reitano
language : en
Publisher: CRC Press
Release Date : 2023-05-23

Foundations Of Quantitative Finance Book Iii The Integrals Of Riemann Lebesgue And Riemann Stieltjes written by Robert R. Reitano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.

Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the advantage these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses. As an investment executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial industry and two decades in education where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the first book in the set. While the set offers a continuous progression through these topics, each title can also be studied independently. Features Extensively referenced to utilize materials from earlier books Presents the theory needed to support advanced applications Supplements previous training in mathematics, with more detailed developments Built from the author's five decades of experience in industry, research, and teaching Published and forthcoming titles in the Robert R. Reitano Quantitative Finance Series: Book I: Measure Spaces and Measurable Functions Book II: Probability Spaces and Random Variables Book III: The Integrals of Lebesgue and (Riemann-)Stieltjes Book IV: Distribution Functions and Expectations Book V: General Measure and Integration Theory Book VI: Densities, Transformed Distributions, and Limit Theorems Book VII: Brownian Motion and Other Stochastic Processes Book VIII: Itô Integration and Stochastic Calculus 1 Book IX: Stochastic Calculus 2 and Stochastic Differential Equations Book X: Classical Models and Applications in Finance