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As a corollary, we obtain that every $K$-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to $\\tilde\\mcC$; this improves a result due to Borwein and Wang. Another corollary is that if $X$ is Asplund, $f:X\\to\\R$ cone mo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0511565","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2005-11-22T16:38:21Z","cross_cats_sorted":[],"title_canon_sha256":"c144565e996d0c620129c3dabb6900035a6c3080f33e83cd81c472a107effae9","abstract_canon_sha256":"0dbd2e8ac848ee97b3894c8015da19e5dd44b5844faae3b5a9a9fb0b3cbb7f81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:51:44.238472Z","signature_b64":"w3/Jhi2pNCVai9e88vBJY+s0i7wpE+bf9I6UwwkWt1MR4EUCYYDukG/BnwQVK71EVLA+2qF/l+tGT7QHT8jxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90c033b8d0dcf3a66a93f8e27e4d8770a237d43024da199598d5c9c937c467d6","last_reissued_at":"2026-07-04T14:51:44.238075Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:51:44.238075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Gateaux differentiability of pointwise Lipschitz mappings","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jakub Duda","submitted_at":"2005-11-22T16:38:21Z","abstract_excerpt":"We prove that for every function $f:X\\to Y$, where $X$ is a separable Banach space and $Y$ is a Banach space with RNP, there exists a set $A\\in\\tilde\\mcA$ such that $f$ is Gateaux differentiable at all $x\\in S(f)\\setminus A$, where $S(f)$ is the set of points where $f$ is pointwise-Lipschitz. 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