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We show that the set of pseudo-physical measures is meager in the space of all invariant measures. Finally, we study the entropy function. We construct pseudo-physical measures with infinite entropy. We also prove that, for each m $\\ge$ 1, there exists infinitely many pseudo-physical measures with entropy log m, and deduce that "},"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":"1705.10133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-29T11:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"605288bf0ae05727f48885d7c62fbf9a95eab16ee10b0b6da87db2d5d052d664","abstract_canon_sha256":"1edcb8c3dfeb137e1abaea92d95e8e2960210f78d87f6fabe199f3dec41bb73f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:31.880779Z","signature_b64":"81gsVRzzE5hrfySnAMr/X2Dt+xpZunoTm2ch3i2PFFkOfxh1Sa3EX/U8K0sPQdwcBvG/7hxHMQhjFm1gmmhiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e43c6a3c1c63d06fe20a4e533370dd17b8d79b29416c3e66241c514c7fc8b38","last_reissued_at":"2026-05-18T00:43:31.880291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:31.880291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo-physical measures for typical continuous maps of the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras (IMERL), Serge Troubetzkoy (I2M)","submitted_at":"2017-05-29T11:50:37Z","abstract_excerpt":"We study the measure theoretic properties of typical C 0 maps of the interval. 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