Abstract: |
Minkowski's theorem relates a subset of
ℝn, the Lebesgue measure, and the
integer lattice ℤn: It states that
any convex subset of ℝn with volume
greater than 2n contains at least one lattice
point from ℤn\{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
ℝn 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_Theorem-AFP,
author = {Manuel Eberl},
title = {Minkowski's Theorem},
journal = {Archive of Formal Proofs},
month = jul,
year = 2017,
note = {\url{http://isa-afp.org/entries/Minkowskis_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}
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