# Minkowski's Theorem

 Title: Minkowski's Theorem Author: Manuel Eberl Submission date: 2017-07-13 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{https://isa-afp.org/entries/Minkowskis_Theorem.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License