[isabelle] new AFP entry: Minkowski's Theorem


Minkowski's Theorem
by Manuel Eberl

Minkowski's theorem relates a subset of â^n, the Lebesgue measure, and the integer lattice â^n: It states that any convex subset of â^n with volume greater than 2^n contains at least one lattice point from â^n\{0}, i.âe. a non-zero point with integer coefficients.

A related theorem which directly implies this is Blichfeldt's theorem, which states that any subset of â^n with a volume greater than 1 contains two different points whose difference vector has integer components.

The entry contains a proof of both theorems.


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