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3. Multidimensional Variations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1834)

Abstract

We define in this chapter the multidimensional variations, study their properties and show how the \(\epsilon\)-entropy of a subset \(A\) of \(\mathbb{R}^n\) can be bounded in terms of variations of \(A\). This form one of the main technical tools used in this book.

Keywords

  • Integral Geometry
  • Homogeneity Property
  • Main Technical Tool
  • Multidimensional Variation
  • Inductive Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Yosef Yomdin .

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© 2004 Springer-Verlag

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Yomdin, Y., Comte, G. (2004). 3. Multidimensional Variations. In: Tame Geometry with Application in Smooth Analysis. Lecture Notes in Mathematics, vol 1834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40960-1_3

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  • DOI: https://doi.org/10.1007/978-3-540-40960-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20612-5

  • Online ISBN: 978-3-540-40960-1

  • eBook Packages: Springer Book Archive