A Course On Borel Sets Graduate Texts In Mathematics 180
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A Course On Borel Sets
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Author : S.M. Srivastava
language : en
Publisher: Springer
Release Date : 2013-12-01
A Course On Borel Sets written by S.M. Srivastava and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirich let and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from con tinuous functions and iterating the operation 0/ pointwise limit on a se quence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire.
A Course On Borel Sets Graduate Texts In Mathematics 180
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Author : Laszlo Gyorfi
language : en
Publisher:
Release Date : 1998
A Course On Borel Sets Graduate Texts In Mathematics 180 written by Laszlo Gyorfi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
A Course on Borel' sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc.
Ergodic Theory
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Author : David Kerr
language : en
Publisher: Springer
Release Date : 2017-02-09
Ergodic Theory written by David Kerr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-09 with Mathematics categories.
This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
Fundamentals Of Set And Number Theory
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Author : Valeriy K. Zakharov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Fundamentals Of Set And Number Theory written by Valeriy K. Zakharov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language
Appalachian Set Theory
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Author : James Cummings
language : en
Publisher: Cambridge University Press
Release Date : 2012-11-15
Appalachian Set Theory written by James Cummings 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 2012-11-15 with Mathematics categories.
Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.
Set Theory
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Author : Simon Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01
Set Theory written by Simon Thomas 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 2002-01-01 with Mathematics categories.
This volume presents the proceedings from the Mid-Atlantic Mathematical Logic Seminar (MAMLS) conference held in honor of Andras Hajnal at the DIMACS Center, Rutgers University (New Brunswick, NJ). Articles include both surveys and high-level research papers written by internationally recognized experts in the field of set theory. Many of the current active areas of set theory are represented in this volume. It includes research papers on combinatorial set theory, set theoretictopology, descriptive set theory, and set theoretic algebra. There are valuable surveys on combinatorial set theory, fragments of the proper forcing axiom, and the reflection properties of stationary sets. The book also includes an exposition of the ergodic theory of lattices in higher rank semisimpleLie groups-essential reading for anyone who wishes to understand much of the recent work on countable Borel equivalence relations.
Meromorphic Dynamics
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Author : Janina Kotus
language : en
Publisher: Cambridge University Press
Release Date : 2023
Meromorphic Dynamics written by Janina Kotus 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 2023 with Functions, Meromorphic categories.
"The first of two volumes provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students"--
Meromorphic Dynamics Volume 1
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Author : Janina Kotus
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-04
Meromorphic Dynamics Volume 1 written by Janina Kotus 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 2023-05-04 with Mathematics categories.
This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students.
Measure And Integration Theory
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Author : Heinz Bauer
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20
Measure And Integration Theory written by Heinz Bauer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.
This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.
Beyond First Order Model Theory Volume I
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Author : Jose Iovino
language : en
Publisher: CRC Press
Release Date : 2017-08-14
Beyond First Order Model Theory Volume I written by Jose Iovino and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.