{"paper":{"title":"Push forward measures and concentration phenomena","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Hugo Jim\\'Enez, M\\'arton Nasz\\'odi, Rafael Villa","submitted_at":"2011-12-20T16:49:18Z","abstract_excerpt":"In this note we study how a concentration phenomenon can be transmitted from one measure $\\mu$ to a push-forward measure $\\nu$. In the first part, we push forward $\\mu$ by $\\pi:supp(\\mu)\\rightarrow \\Ren$, where $\\pi x=\\frac{x}{\\norm{x}_L}\\norm{x}_K$, and obtain a concentration inequality in terms of the medians of the given norms (with respect to $\\mu$) and the Banach-Mazur distance between them. This approach is finer than simply bounding the concentration of the push forward measure in terms of the Banach-Mazur distance between $K$ and $L$. As a corollary we show that any normed probability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4765","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"}