{"paper":{"title":"A Refinement of the Kolmogorov-Marcinkiewicz-Zygmund 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, Yongcheng Qi","submitted_at":"2010-08-25T19:09:59Z","abstract_excerpt":"For the partial sums formed from a sequence of i.i.d. random variables having a finite absolute p'th moment for some p in (0,2), we extend the recent and striking discovery of Hechner and Heinkel (Journal of Theoretical Probability (2010)) concerning \"complete moment convergence\" to the two cases 0<p<1 and p=1. Moreover, for 0<p<2, we obtain \"almost sure convergence\" analogues of these \"complete moment convergence\" results and these \"almost sure convergence\" analogues may be regarded as being a refinement of the celebrated Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers. Versions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4341","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"}