Abstract: 
Minkowski's theorem relates a subset of
ℝ^{n}, the Lebesgue measure, and the
integer lattice ℤ^{n}: It states that
any convex subset of ℝ^{n} with volume
greater than 2^{n} contains at least one lattice
point from ℤ^{n}\{0}, i. e. a
nonzero point with integer coefficients. A
related theorem which directly implies this is Blichfeldt's
theorem, which states that any subset of
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. 
BibTeX: 
@article{Minkowskis_TheoremAFP,
author = {Manuel Eberl},
title = {Minkowski's Theorem},
journal = {Archive of Formal Proofs},
month = jul,
year = 2017,
note = {\url{http://isaafp.org/entries/Minkowskis_Theorem.shtml},
Formal proof development},
ISSN = {2150914x},
}
