{"paper":{"title":"Lipschitz functions on the infinite-dimensional torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Bo'az Klartag, Dmitry Faifman","submitted_at":"2014-11-06T14:08:59Z","abstract_excerpt":"We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that $f$ is a measurable, real-valued, Lipschitz function on the torus $\\mathbb{T}^{\\infty}$. We prove that there exists a number $a \\in \\mathbb R$ with the following property: For any $\\epsilon > 0$ there exists a parallel, infinite-dimensional subtorus $M \\subseteq \\mathbb T^{\\infty}$ such that the restriction of the function $f-a$ to the subtorus $M$ has an $L^{\\infty}(M)$-norm of at most $\\epsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1620","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"}