{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FUSAVRQUAU7JNO2LPO47SYC25","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95"},"schema_version":"1.0","source":{"id":"1510.08801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08801v1","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"pith_short_12","alias_value":"3FUSAVRQUAU7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FUSAVRQUAU7JNO2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FUSAVRQ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4","target":"graph","created_at":"2026-05-18T01:28:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space $X$ is said to have the weak Lebesgue property if every Riemann integrable function from $[0,1]$ into $X$ is weakly continuous almost everywhere. We prove that the weak Lebesgue property is stable under $\\ell_1$-sums and obtain new examples of Banach spaces with and without this property. Furthermore, we characterize Dunford-Pettis operators in terms of Riemann integrability and provide a quantitative result about the size of the set of $\\tau$-continuous non Riemann integrable functions, wi","authors_text":"Gonzalo Mart\\'inez-Cervantes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title":"Riemann integrability versus weak continuity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08801","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c","target":"record","created_at":"2026-05-18T01:28:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95"},"schema_version":"1.0","source":{"id":"1510.08801","kind":"arxiv","version":1}},"canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","first_computed_at":"2026-05-18T01:28:26.685803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:26.685803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9v8NQzKuNZOrcSMAyczY3wpCmCk6f5VLJUBZF5rb5phXjnCqu0/bXs39f9i2e84QzH7FcbpkzFXyNOmSVPooCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:26.686391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c","sha256:7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4"],"state_sha256":"612ff4b52d62372ebc558ce495c2e4f53484a7b322caa9cd76aa1386c22b3077"}