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\title{Minkowski's Theorem}
\author{Manuel Eberl}
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\begin{abstract}
	Minkowski's theorem relates a subset of $\mathbb{R}^n$, the Lebesgue measure, and the integer lattice $\mathbb{Z}^n$: It states that any convex subset of $\mathbb{R}^n$ with volume greater than $2^n$ contains at least one lattice point from $\mathbb{Z}^n\setminus\{0\}$, i.\,e. a non-zero point with integer coefficients.

	A related theorem which directly implies this is Blichfeldt's theorem, which states that any subset of $\mathbb{R}^n$ 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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