{"paper":{"title":"A probability inequality for sums of independent Banach space valued random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Rosalsky, Deli Li, Han-Ying Liang","submitted_at":"2017-03-22T21:56:26Z","abstract_excerpt":"Let $(\\mathbf{B}, \\|\\cdot\\|)$ be a real separable Banach space. Let $\\varphi(\\cdot)$ and $\\psi(\\cdot)$ be two continuous and increasing functions defined on $[0, \\infty)$ such that $\\varphi(0) = \\psi(0) = 0$, $\\lim_{t \\rightarrow \\infty} \\varphi(t) = \\infty$, and $\\frac{\\psi(\\cdot)}{\\varphi(\\cdot)}$ is a nondecreasing function on $[0, \\infty)$. Let $\\{V_{n};~n \\geq 1 \\}$ be a sequence of independent and symmetric {\\bf B}-valued random variables. In this note, we establish a probability inequality for sums of independent {\\bf B}-valued random variables by showing that for every $n \\geq 1$ and a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07868","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"}