{"paper":{"title":"On the regular convergence of multiple series of numbers and multiple integrals of locally integrable functions over $\\bar{\\R}^m_+$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ferenc Moricz","submitted_at":"2011-12-21T08:40:15Z","abstract_excerpt":"We investigate the regular convergence of the $m$-multiple series $$\\sum^\\infty_{j_1=0} \\sum^\\infty_{j_2=0}...\\sum^\\infty_{j_m=0} \\ c_{j_1, j_2,..., j_m}\\leqno(*)$$ of complex numbers, where $m\\ge 2$ is a fixed integer. We prove Fubini's theorem in the discrete setting as follows. If the multiple series (*) converges regularly, then its sum in Pringsheim's sense can be computed by successive summation.\n  We introduce and investigate the regular convergence of the $m$-multiple integral $$\\int^\\infty_0 \\int^\\infty_0...\\int^\\infty_0 f(t_1, t_2,..., t_m) dt_1 dt_2...dt_m,\\leqno(**)$$ where $f: \\ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4950","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"}