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Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206
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Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206
Get Book Here
Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author: Richard Wheeden
Publisher: CRC Press
ISBN: 1482229536
Category : Mathematics
Languages : en
Pages : 289
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Book Description
This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Author: Jack Campbell (Naval officer)
Publisher:
ISBN: 9781596065680
Category : Alternative histories (Fiction)
Languages : en
Pages : 0
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Book Description
"In a transformed mid-nineteenth century America dominated by plantation owners and kept in line by Southern military forces, a mild-mannered academic from Maine, Professor Joshua Chamberlain, stands accused of crimes against the nation. In court alongside him is Abraham Lincoln, whose fiery rhetoric brands him a 'threat to the security of the United States of America.' Convicted, Chamberlain is sentenced to forty years hard labor, while Lincoln s fate is indefinite detention at Fortress Monroe. But Professor Chamberlain then encounters military minds who understand the true ideals upon which the country was founded and who want to foment revolution. To succeed, they need a leader, someone to inspire the people to take up the cause of liberty: Lincoln. All they have to do is flawlessly execute a daring plan to rescue him from the darkest federal prison"--Jacket.
Author: Lakhdar Aggoun
Publisher: Cambridge University Press
ISBN: 9781139456241
Category : Mathematics
Languages : en
Pages : 274
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Book Description
The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers.
Author: Jeff Shaara
Publisher: Ballantine Books
ISBN: 0345438507
Category : Fiction
Languages : en
Pages : 578
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Book Description
In the Pulitzer prize–winning classic The Killer Angels, Michael Shaara created the finest Civil War novel of our time. The Last Full Measure tells the epic story of the events following the Battle of Gettysburg and brings to life the final two years of the Civil War. Jeff Shaara dramatizes the escalating confrontation between Robert E. Lee and Ulysses S. Grant—complicated, heroic, and deeply troubled men. For Lee and his Confederate forces, Gettysburg has been an unspeakable disaster, but he is determined to fight to the bitter end; he faces Grant, the decisive, hard-nosed leader the Union army so desperately needs in order to turn the tide of the war. From the costly Battle of the Wilderness to the agonizing seize of Petersburg to Lee’s epoch-making surrender at Appomattox, Shaara portrays the riveting conclusion of the Civil War through the minds and hearts of the individuals who gave their last full measure. BONUS: This edition includes an excerpt from Jeff Shaara's Blaze of Glory.
Author: Sheldon Axler
Publisher: Springer Nature
ISBN: 3030331431
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
Author: Herbert Federer
Publisher: Springer
ISBN: 3642620108
Category : Mathematics
Languages : en
Pages : 694
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Book Description
"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)
Author: Clayton M. Christensen
Publisher: Harvard Business Review Press
ISBN: 1633692574
Category : Business & Economics
Languages : en
Pages : 28
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Book Description
In the spring of 2010, Harvard Business School’s graduating class asked HBS professor Clay Christensen to address them—but not on how to apply his principles and thinking to their post-HBS careers. The students wanted to know how to apply his wisdom to their personal lives. He shared with them a set of guidelines that have helped him find meaning in his own life, which led to this now-classic article. Although Christensen’s thinking is rooted in his deep religious faith, these are strategies anyone can use. Since 1922, Harvard Business Review has been a leading source of breakthrough ideas in management practice. The Harvard Business Review Classics series now offers you the opportunity to make these seminal pieces a part of your permanent management library. Each highly readable volume contains a groundbreaking idea that continues to shape best practices and inspire countless managers around the world.
Author: D. H. Fremlin
Publisher: Torres Fremlin
ISBN: 0953812928
Category : Fourier analysis
Languages : en
Pages : 563
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Book Description
Author: Trent Reedy
Publisher: Arthur A. Levine Books
ISBN: 9780545548786
Category : Civil war
Languages : en
Pages : 0
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Book Description
Trent Reedy brings his action-packed, provocative trilogy about the second American Civil War to a stunning and stirring close in The Last Full Measure
