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Integer Points in Parallelepipeds

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Part of the Lecture Notes in Mathematics book series (LNM, volume 785)

Abstract

Let K be a compact convex set in En, symmetric about \( \mathop 0\limits_ = \), and suppose that \( \mathop 0\limits_ = \) lies in the interior of K. We call such a set a convex body. Let V(K) denote the volume of K. (By the volume of K we mean the Riemann integral of the characteristic function of K. It can be proved that every convex body has a volume in this sense. Alternatively, the existence of the volume of K may be added as a hypothesis.)

Keywords

Linear Form Unit Ball Convex Body Integer Point Symmetric Convex 
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References

  1. H. Minkowski (1896 & 1910). Geometrie der Zahlen. Teubner: Leipzig u. Berlin (The 1910 ed. prepared posthumously by Hilbert and Speiser).Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

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