{"paper":{"title":"On linearity of pan-integral and pan-integrable functions space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jun Li, Radko Mesiar, Yao Ouyang","submitted_at":"2016-12-06T05:48:21Z","abstract_excerpt":"$L\\sp{p}$ space is a crucial aspect of classical measure theory. For nonadditive measure, it is known that $L\\sp{p}$ space theory holds for the Choquet integral whenever the monotone measure $\\mu$ is submodular and continuous from below. The main purpose of this paper is to generalize $L\\sp{p}$ space theory to $+,\\cdot$-based pan-integral. Let $(X, {\\cal A}, \\mu)$ be a monotone measure space. We prove that the $+,\\cdot$-based pan-integral is additive with respect to integrands if $\\mu$ is subadditive. Then we introduce the pan-integral for real-valued functions(not necessarily nonnegative), an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01673","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"}