{"paper":{"title":"An Extension of Feller's Strong Law of Large Numbers","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":"2017-03-24T17:11:26Z","abstract_excerpt":"~This paper presents a general result that allows for establishing a link between the Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers and Feller's strong law of large numbers in a Banach space setting. Let $\\{X, X_{n}; n \\geq 1\\}$ be a sequence of independent and identically distributed Banach space valued random variables and set $S_{n} = \\sum_{i=1}^{n}X_{i},~n \\geq 1$. Let $\\{a_{n}; n \\geq 1\\}$ and $\\{b_{n}; n \\geq 1\\}$ be increasing sequences of positive real numbers such that $\\lim_{n \\rightarrow \\infty} a_{n} = \\infty$ and $\\left\\{b_{n}/a_{n};~ n \\geq 1 \\right\\}$ is a nondecr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08512","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"}