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Author: Sy David Friedman
Publisher: American Mathematical Society
ISBN: 1470442965
Category : Mathematics
Languages : en
Pages : 150
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Book Description
The authors prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $Delta^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.
Author: Sy David Friedman
Publisher: American Mathematical Society
ISBN: 1470442965
Category : Mathematics
Languages : en
Pages : 150
Get Book Here
Book Description
The authors prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $Delta^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.
Author: Vladimir I. Bogachev
Publisher: Springer Science & Business Media
ISBN: 3540345140
Category : Mathematics
Languages : en
Pages : 1075
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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: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 0821842250
Category : Mathematics
Languages : en
Pages : 458
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Book Description
George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Author: Matthew Foreman
Publisher: Springer Science & Business Media
ISBN: 1402057644
Category : Mathematics
Languages : en
Pages : 2200
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Book Description
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Author: Christoph Bandt
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This volume contains surveys and original papers resulting from the international conference Topology and Measure VI.
Author: Rajendra Bhatia
Publisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137
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Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Author:
Publisher: World Scientific
ISBN: 9814324353
Category :
Languages : en
Pages : 814
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Book Description
Author: Chao Wang
Publisher: American Mathematical Soc.
ISBN: 1470446898
Category : Education
Languages : en
Pages : 119
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Book Description
In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Author: Patrick Delorme
Publisher: American Mathematical Soc.
ISBN: 147044402X
Category : Education
Languages : en
Pages : 102
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Book Description
Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].
Author: Alexander Kharazishvili
Publisher: Springer Nature
ISBN: 3031170334
Category : Mathematics
Languages : en
Pages : 256
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Book Description
This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
