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Record Nr. |
UNINA9910144619803321 |
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Autore |
Yomdin Yosef |
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Titolo |
Tame Geometry with Application in Smooth Analysis / / by Yosef Yomdin, Georges Comte |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 |
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ISBN |
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Edizione |
[1st ed. 2004.] |
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Descrizione fisica |
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1 online resource (CC, 190 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1834 |
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Disciplina |
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Soggetti |
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Geometry, Algebraic |
Measure theory |
Functions of real variables |
Functions of complex variables |
Algebraic Geometry |
Measure and Integration |
Real Functions |
Several Complex Variables and Analytic Spaces |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages 173-186). |
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Nota di contenuto |
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Preface -- Introduction and Content -- Entropy -- Multidimensional Variations -- Semialgebraic and Tame Sets -- Some Exterior Algebra -- Behavior of Variations under Polynomial Mappings -- Quantitative Transversality and Cuspidal Values for Polynomial Mappings -- Mappings of Finite Smoothness -- Some Applications and Related Topics -- Glossary -- References. |
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Sommario/riassunto |
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The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. |
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