On Measures of Information and Their Characterizations


Book Description

This book deals with measures of information (the most important ones being called entropies), their properties, and, reciprocally, with questions concerning which of these properties determine known measures of information, and which are the most general formulas satisfying reasonable requirements on practical measures of information. Thisis the first book investigating this subject in depth.




Characterizations of Information Measures


Book Description

"This book is highly recommended for all those whose interests lie in the fields that deal with any kind of information measures. It will also find readers in the field of functional analysis..".Mathematical Reviews




The Mathematical Theory of Communication


Book Description

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.




An Introduction to Measure Theory


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.




Approaches to the Development of Character


Book Description

The development of character is a valued objective for many kinds of educational programs that take place both in and outside of school. Educators and administrators who develop and run programs that seek to develop character recognize that the established approaches for doing so have much in common, and they are eager to learn about promising practices used in other settings, evidence of effectiveness, and ways to measure the effectiveness of their own approaches. In July 2016, the National Academies of Sciences, Engineering, and Medicine held a workshop to review research and practice relevant to the development of character, with a particular focus on ideas that can support the adults who develop and run out-of-school programs. This publication summarizes the presentations and discussions from the workshop.




Character Strengths and Virtues


Book Description

"Character" has become a front-and-center topic in contemporary discourse, but this term does not have a fixed meaning. Character may be simply defined by what someone does not do, but a more active and thorough definition is necessary, one that addresses certain vital questions. Is character a singular characteristic of an individual, or is it composed of different aspects? Does character--however we define it--exist in degrees, or is it simply something one happens to have? How can character be developed? Can it be learned? Relatedly, can it be taught, and who might be the most effective teacher? What roles are played by family, schools, the media, religion, and the larger culture? This groundbreaking handbook of character strengths and virtues is the first progress report from a prestigious group of researchers who have undertaken the systematic classification and measurement of widely valued positive traits. They approach good character in terms of separate strengths-authenticity, persistence, kindness, gratitude, hope, humor, and so on-each of which exists in degrees. Character Strengths and Virtues classifies twenty-four specific strengths under six broad virtues that consistently emerge across history and culture: wisdom, courage, humanity, justice, temperance, and transcendence. Each strength is thoroughly examined in its own chapter, with special attention to its meaning, explanation, measurement, causes, correlates, consequences, and development across the life span, as well as to strategies for its deliberate cultivation. This book demands the attention of anyone interested in psychology and what it can teach about the good life.




The Theory of Quantum Information


Book Description

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.




Measure for Measure


Book Description

Since the rediscovery of Elizabethan stage conditions early this century, admiration for Measure for Measure has steadily risen. It is now a favorite with the critics and has attracted widely different styles of performance. At one extreme the play is seen as a religious allegory, at the other it has been interpreted as a comedy protesting against power and privilege. Brian Gibbons focuses on the unique tragi-comic experience of watching the play, the intensity and excitement offered by its dramatic rhythm, the reversals and surprises that shock the audience even to the end. The introduction describes the play's critical reception and stage history and how these have varied according to prevailing social, moral and religious issues, which were highly sensitive when Measure for Measure was written, and have remained so to the present day.




Markov Processes


Book Description

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference." -American Scientist "There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook." -Journal of Statistical Physics Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.




The Measure


Book Description

INSTANT NEW YORK TIMES BESTSELLER - The Read With Jenna Today Show Book Club Pick! "A story of love and hope as interweaving characters display: how all moments, big and small, can measure a life. If you want joy, love, romance, and hope—read with us." —Jenna Bush Hager A luminous, spirit-lifting blockbuster that asks: would you choose to find out the length of your life? Eight ordinary people. One extraordinary choice. It seems like any other day. You wake up, drink a cup of coffee, and head out. But today, when you open your front door, waiting for you is a small wooden box. The contents of this mysterious box tells you the exact number of years you will live. From suburban doorsteps to desert tents, every person on every continent receives the same box. In an instant, the world is thrust into a collective frenzy. Where did these boxes come from? What do they mean? Is there truth to what they promise? As society comes together and pulls apart, everyone faces the same shocking choice: Do they wish to know how long they’ll live? And, if so, what will they do with that knowledge? The Measure charts the dawn of this new world through an unforgettable cast of characters whose decisions and fates interweave with one another: best friends whose dreams are forever entwined, pen pals finding refuge in the unknown, a couple who thought they didn’t have to rush, a doctor who cannot save himself, and a politician whose box becomes the powder keg that ultimately changes everything. Enchanting and deeply uplifting, The Measure is an ambitious, invigorating story about family, friendship, hope, and destiny that encourages us to live life to the fullest.