{"paper":{"title":"Statistical convergence of order $\\alpha$ in probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pratulananda Das, Sanjoy Ghosal, Sumit Som","submitted_at":"2016-05-18T12:42:59Z","abstract_excerpt":"In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\\alpha$ in probability, strong $p$-Ces$\\grave{\\mbox{a}}$ro summability of order $\\alpha$ in probability, lacunary statistical convergence or $S_{\\theta}$-convergence of order $\\alpha$ in probability, ${N_{\\theta}}$-convergence of order $\\alpha$ in probability have been introduced and their certain basic properties have been studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05555","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"}