{"paper":{"title":"A Tauberian theorem for ideal statistical convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Marek Balcerzak, Paolo Leonetti","submitted_at":"2019-08-13T20:49:06Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on the positive integers, a real sequence $(x_n)$ is said to be $\\mathcal{I}$-statistically convergent to $\\ell$ provided that $$ \\textstyle \\left\\{n \\in \\mathbf{N}: \\frac{1}{n}|\\{k \\le n: x_k \\notin U\\}| \\ge \\varepsilon\\right\\} \\in \\mathcal{I} $$ for all neighborhoods $U$ of $\\ell$ and all $\\varepsilon>0$. First, we show that $\\mathcal{I}$-statistical convergence coincides with $\\mathcal{J}$-convergence, for some unique ideal $\\mathcal{J}=\\mathcal{J}(\\mathcal{I})$. In addition, $\\mathcal{J}$ is Borel [analytic, coanalytic, respectively] whenever $\\mathcal{I}$ is B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04853","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}