Israel Journal of Mathematics

, Volume 128, Issue 1, pp 1–27 | Cite as

Isometric approximation property in euclidean spaces

  • Jussi Väisälä


We give a necessary and sufficient quantitative geometric condition for a compact setA⊂R n to have the following property with a givenc≥1: For everyɛ>0 and for every mapf: A→R n such that\(\left| {\left| {fx - fy} \right| - \left| {x - y} \right|} \right| \leqslant \varepsilon for all x,y \in A\) there is an isometryS: A→R n such that |Sxfx|≤ for allxA.


EUCLIDEAN Space Solar System Orthogonal Projection Piecewise Linear Function Maximal Sequence 
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Copyright information

© The Hebrew University Magnes Press 2002

Authors and Affiliations

  • Jussi Väisälä
    • 1
  1. 1.Matematiikan laitosHelsingin yliopistoHelsinkiFinland

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