{"paper":{"title":"Integrable solutions of inhomogeneous refinement type equations on intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Janusz Morawiec, Rafa{\\l} Kapica","submitted_at":"2015-07-27T13:38:45Z","abstract_excerpt":"Given a probability measure $P$ on a $\\sigma$-algebra of subsets of a set $\\Omega$, an interval $I\\subset\\mathbb R$, $g\\in L^1(I)$, and a function $\\varphi\\colon I\\times\\Omega\\to I$ fulfilling some conditions we obtain results on the existence of solutions $f\\in L^1(I)$ of the inhomogeneous refinement type equation $$ f(x)=\\int_{\\Omega}\\big|\\varphi'_x(x,\\omega)\\big|f(\\varphi(x,\\omega))dP(\\omega)+g(x). $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07401","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"}