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Analytic sets. --- Ensembles analytiques. --- Ensembles, Théorie descriptive des
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Analytic sets. --- Ensembles analytiques. --- Ensembles, Théorie descriptive des
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Analytic sets. --- Ensembles analytiques. --- Analyse fonctionnelle --- Functional analysis. --- Mesure, Théorie de la
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Analytic Sets in Locally Convex Spaces
Analytic sets. --- Locally convex spaces. --- Spaces, Locally convex --- Linear topological spaces --- Sets, Analytic --- Analytic spaces --- Set theory
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Algebraic geometry --- Algebraic topology --- Semialgebraic sets. --- Semianalytic sets. --- Ensembles semi-algébriques. --- Ensembles semi-analytiques. --- Semialgebraic sets --- Semianalytic sets --- Semi-analytic sets --- Geometry, Algebraic --- Set theory
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Mathematical logic --- Descriptive set theory --- Analytic spaces --- Game theory --- 515.12 --- Analytic sets --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Set theory --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Sets, Analytic --- General topology --- Analytic sets. --- Analytic spaces. --- Descriptive set theory. --- Game theory. --- 515.12 General topology --- Ensembles analytiques. --- Théorie des ensembles --- Théorie des ensembles. --- Set theory. --- Théorie des ensembles --- Ensembles, Théorie descriptive des
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Vitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 6-8 of this carefully written text present a major recent accomplishment of modern complex analysis, the affirmative resolution of this conjecture. Four of the five mathematicians whose work solved Vitushkin's conjecture have won the prestigious Salem Prize in analysis. Chapters 1-5 of this book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. Although standard notation is used throughout, there is a symbol glossary at the back of the book for the reader's convenience. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.
Analytic functions. --- Analytic sets. --- Set theory. --- Analytic functions --- Analytic sets --- Set theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Sets, Analytic --- Mathematics. --- Functions of complex variables. --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Functions of complex variables --- Series, Taylor's --- Logic, Symbolic and mathematical --- Analytic spaces --- Differential equations, partial. --- Partial differential equations
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Mathematical logic --- 510.2 --- Foundations of mathematics --- 510.2 Foundations of mathematics --- Descriptive set theory. --- Forcing (Model theory) --- Continuum hypothesis --- Borel sets. --- Borel sets --- Descriptive set theory --- Model theory --- Set theory --- Generalized continuum hypothesis --- Hypothesis, Continuum --- Hypothesis, Generalized continuum --- B-measurable sets --- B-sets --- Borel-measurable sets --- Borel subsets --- Borelian sets --- Subsets, Borel --- Analytic sets --- Topology
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Set theory --- Descriptive set theory --- Forcing (Model theory) --- Borel sets --- B-measurable sets --- B-sets --- Borel-measurable sets --- Borel subsets --- Borelian sets --- Subsets, Borel --- Analytic sets --- Topology --- Model theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Borel sets.
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