{"paper":{"title":"Lattice coverings and gaussian measures of n-dimensional convex bodies","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Stanislaw J. Szarek, W. Banaszczyk","submitted_at":"1995-03-20T00:00:00Z","abstract_excerpt":"Let $\\| \\cdot \\|$ be the euclidean norm on ${\\bf R}^n$ and $\\gamma_n$ the (standard) Gaussian measure on ${\\bf R}^n$ with density $(2 \\pi )^{-n/2} e^{- \\| x\\|^2 /2}$. Let $\\vartheta$ ($ \\simeq 1.3489795$) be defined by $\\gamma_1 ([ - \\vartheta /2, \\vartheta /2]) = 1/2$ and let $L$ be a lattice in ${\\bf R}^n$ generated by vectors of norm $\\leq \\vartheta$. Then, for any closed convex set $V$ in ${\\bf R}^n$ with $\\gamma_n (V) \\geq \\frac{1}{2}$ and for any $a \\in {\\bf R}^n$, $(a +L) \\cap V \\neq \\phi$. The above statement can be viewed as a ``nonsymmetric'' version of Minkowski Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9503214","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}