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The Venkov-McMullen Theorem and Stein’s Phenomenon

  • Chuanming Zong
  • James J. Dudziak
Part of the Universitext book series (UTX)

Abstract

Let M be an n-dimensional compact set with interior points. If there exists a set of points X such that
$$\bigcup\limits_{x \in X} {\left( {M + x} \right)} = {R^n}$$
and
$$\left( {\operatorname{int} \left( M \right) + {x_1}} \right) \cap \left( {\operatorname{int} \left( M \right) + {x_2}} \right) = 0$$
whenever x1, x2X with x1x2, then we call M a translative tile. In addition, if X is a lattice in R n , then we call M a lattice tile.

Keywords

Convex Body Area Function Relative Interior Convex Polytope Positive Borel Measure 
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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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Chuanming Zong
    • 1
  • James J. Dudziak
    • 2
  1. 1.Institute of MathematicsThe Chinese Academy of SciencesBeijingPR China
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA

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