Author: Rachel Fletcher Publisher: George F Thompson Publishing ISBN: 9781938086021 Category : Architectural design Languages : en Pages : 0
Book Description
The desire for harmony is universal among all cultures. In Infinite Measure, we rediscover a fundamental starting point for designers of all ages: the simple act of drawing with a compass and a rule can sensitize the designer to the rich subtleties of spatial harmony, no matter how one ultimately chooses to express it.
Author: Jon Aaronson Publisher: American Mathematical Soc. ISBN: 0821804944 Category : Mathematics Languages : en Pages : 298
Book Description
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
Author: Alan J. Weir Publisher: Cambridge University Press ISBN: 9780521097512 Category : Mathematics Languages : en Pages : 300
Book Description
A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.
Author: Vladimir I. Bogachev Publisher: Springer Science & Business Media ISBN: 3540345140 Category : Mathematics Languages : en Pages : 1075
Book Description
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Author: Carlos S Kubrusly Publisher: Gulf Professional Publishing ISBN: 9780123708991 Category : Mathematics Languages : en Pages : 184
Book Description
This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises. JARGON BUSTER: measure theory Measure theory investigates the conditions under which integration can take place. It considers various ways in which the "size" of a set can be estimated. This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering. Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra) Includes 140 classical measure-theory problems Carefully crafted to present essential elements of the theory in compact form
Author: Yurij M. Berezansky Publisher: Birkhäuser ISBN: 3034891857 Category : Mathematics Languages : en Pages : 443
Book Description
"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.
Author: Morgan Publisher: Routledge ISBN: 1351423797 Category : Mathematics Languages : en Pages : 300
Book Description
Investigations by Baire, Lebesgue, Hausdorff, Marczewski, and othes have culminated invarious schemes for classifying point sets. This important reference/text bringstogether in a single theoretical framework the properties common to these classifications.Providing a clear, thorough overview and analysis of the field, Point Set Theoryutilizes the axiomatically determined notion of a category base for extending generaltopological theorems to a higher level of abstraction ... axiomatically unifies analogiesbetween Baire category and Lebesgue measure . .. enhances understanding of thematerial with numerous examples and discussions of abstract concepts ... and more.Imparting a solid foundation for the modem theory of real functions and associated areas,this authoritative resource is a vital reference for set theorists, logicians, analysts, andresearch mathematicians involved in topology, measure theory, or real analysis. It is anideal text for graduate mathematics students in the above disciplines who havecompleted undergraduate courses in set theory and real analysis.
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Author: Rachel Fletcher
Author: Terence Tao
Author: Jon Aaronson
Author: D. H. Fremlin
Author: Alan J. Weir
Author: Vladimir I. Bogachev
Author: Carlos S Kubrusly
Author: Gerald A. Edgar
Author: Yurij M. Berezansky
Author: Morgan