{"paper":{"title":"On the relation between Lebesgue summability and some other summation methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jasson Vindas","submitted_at":"2013-05-01T15:21:20Z","abstract_excerpt":"It is shown that if $$ \\sum_{n=1}^{N}n\\left|c_{n}\\right|=O(N), $$ then Lebesgue summability, $(\\mathrm{C},\\beta)$ summability ($\\beta>0$), Abel summability, Riemann summability, and $(\\gamma,\\kappa)$ summability ($\\kappa\\geq 1$) of the series $\\sum_{n=0}^{\\infty}c_{n}$ are all equivalent to one another."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0200","kind":"arxiv","version":2},"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"}