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  • 35e9550ff2 Added the continuous functional calculus. Bokuan Li 2026-07-03 15:21:33 -04:00
  • 683b822e7e Added Gelfand Naimark. Bokuan Li 2026-07-02 14:02:26 -04:00
  • dd62fbc0f4 Label typo? Bokuan Li 2026-07-02 13:12:05 -04:00
  • 1caa2785ef Small adjustments. Bokuan Li 2026-07-01 00:04:11 -04:00
  • 89ec2234be Fixed typo. Bokuan Li 2026-06-30 19:34:11 -04:00
  • 1f9e0bea78 Added extremely disconnected spaces. Bokuan Li 2026-06-30 19:32:42 -04:00
  • 36f5b22042 Added localisable order completeness. Bokuan Li 2026-06-30 16:47:50 -04:00
  • 60544ea6a0 Added some spectrum gruntwork. Bokuan Li 2026-06-30 16:12:33 -04:00
  • e19a5e3ad0 Swapped in vocabulary. Bokuan Li 2026-06-30 14:14:44 -04:00
  • 8090f060d3 Added local L^p spaces. Bokuan Li 2026-06-30 14:13:58 -04:00
  • 98127388ec Retracted localisable version of Radon-Nikodym. Bokuan Li 2026-06-30 13:42:43 -04:00
  • baa048507b Added the localisable version of the radon-nikodym theorem. Bokuan Li 2026-06-29 21:29:57 -04:00
  • 1ab81b49bc RETRACTION ON LCH EMBARRASSING TYPO Bokuan Li 2026-06-29 21:07:59 -04:00
  • 38099f1b19 Added elements of localisable measures. Bokuan Li 2026-06-29 20:55:01 -04:00
  • 831acc66cc Added gluing for measures in terms of scaffoldings. Bokuan Li 2026-06-29 19:29:18 -04:00
  • 26c4bbbb51 LCH typo fix? Bokuan Li 2026-06-29 19:09:55 -04:00
  • ff22fad2f8 Updated the existing system to accomodate scaffolds. Bokuan Li 2026-06-29 17:43:02 -04:00
  • 3ba0eee08d Introduced scaffold to localisable measure spaces. Bokuan Li 2026-06-29 16:57:59 -04:00
  • 671e8984c7 Added the scaffold. Bokuan Li 2026-06-29 16:49:35 -04:00
  • a11cfe4e04 Book keeping. Bokuan Li 2026-06-29 16:34:06 -04:00
  • 65a2b4cef4 FIxed up lattices. Bokuan Li 2026-06-29 12:37:13 -04:00
  • d4578960f3 Adjustments added to LCH spaces. Bokuan Li 2026-06-29 12:28:30 -04:00
  • 17154547df More minor adjustments. Bokuan Li 2026-06-28 23:11:52 -04:00
  • 35be74f8af Refined the approximation argument. Bokuan Li 2026-06-28 23:07:23 -04:00
  • a7904bd32c More typo fix. Bokuan Li 2026-06-28 22:48:14 -04:00
  • 06d3f994f6 Style adjustments in gluing lemma. Bokuan Li 2026-06-28 21:45:48 -04:00
  • c484cd172b Typo fix. Bokuan Li 2026-06-28 21:33:06 -04:00
  • 5abdf6ab3d Fixed wrong reference. Bokuan Li 2026-06-28 21:30:09 -04:00
  • 8f06eca274 One more remark. Bokuan Li 2026-06-28 20:48:46 -04:00
  • 145f3193be Minor sharpening of statements. Bokuan Li 2026-06-28 20:22:35 -04:00
  • 2423cff867 Minor adjustment. Bokuan Li 2026-06-28 20:11:36 -04:00
  • 3d1e095e82 Fixed typos in the gluing lemma. Bokuan Li 2026-06-28 20:10:25 -04:00
  • 4226adf856 Added first darft of gluing lemma for measurable functions. Bokuan Li 2026-06-28 19:50:05 -04:00
  • 3a4f4b46e8 Added the theory of admissible approximant functions. Bokuan Li 2026-06-28 19:29:22 -04:00
  • 121033cfb6 Fixed label typo. Bokuan Li 2026-06-28 14:35:23 -04:00
  • 1d740724b4 Strengthened the simple function approximations. Bokuan Li 2026-06-28 14:33:32 -04:00
  • 4acc8fdf31 Un-retracted some things. Bokuan Li 2026-06-28 12:05:22 -04:00
  • bbff684bd1 Polish correction. Bokuan Li 2026-06-28 12:04:51 -04:00
  • 55bd2e4859 Fixed typo. Bokuan Li 2026-06-27 22:41:48 -04:00
  • d8f56ef537 RETRACTION: SEPARABILITY REQUIRED TO DEFINE CONVERGENCE IN MEASURE Bokuan Li 2026-06-27 22:38:39 -04:00
  • ce52ac4b63 Edited the open preimage functions. Bokuan Li 2026-06-27 22:35:32 -04:00
  • 4616ac2861 First draft for open preimage functions. Bokuan Li 2026-06-27 22:06:50 -04:00
  • 80f79fb30d Added preimage functions. Bokuan Li 2026-06-27 18:41:06 -04:00
  • 48a0e63f61 Added elementary facts about localisable measure spaces. Bokuan Li 2026-06-27 17:11:57 -04:00
  • 3d9c47bda1 Minor housekeeping. Bokuan Li 2026-06-27 14:12:40 -04:00
  • 968fbe6eba Added the support function. Bokuan Li 2026-06-27 13:17:45 -04:00
  • eed3a342e4 Typo fixes. Bokuan Li 2026-06-26 12:59:13 -04:00
  • 369a1e72db Adjustment in Fenchl-Moreau. Bokuan Li 2026-06-26 12:57:30 -04:00
  • 03e7899904 Added the Mackey-Arens theorem (for real). Bokuan Li 2026-06-26 00:45:59 -04:00
  • fbdf280f11 Fixed gap in maximum modulus strip. Bokuan Li 2026-06-26 00:44:31 -04:00
  • 91752ee561 Added compact definition. Bokuan Li 2026-06-26 00:17:28 -04:00
  • 9c08e0a525 Added the Mackey-Arens theorem. Bokuan Li 2026-06-26 00:16:36 -04:00
  • 061a4f3034 More prose corrections. Bokuan Li 2026-06-25 19:22:37 -04:00
  • 98f96b2af1 Performed more housekeeping for the Legendre transform. Bokuan Li 2026-06-25 19:16:16 -04:00
  • 4b404d40a6 Updated the A-A theorem to include convergence on a dense subset. Bokuan Li 2026-06-25 13:58:38 -04:00
  • b7f93c1110 Updated the legendre corollary. Bokuan Li 2026-06-25 13:32:44 -04:00
  • 2c4a8c9d22 Typo fixes for the separable dual lemma. Bokuan Li 2026-06-25 13:17:05 -04:00
  • 83072f4ba4 Adjusted the Legendre sectoin. Bokuan Li 2026-06-25 13:03:51 -04:00
  • c19aaf7fe3 Fixed infinity problem. Bokuan Li 2026-06-25 12:23:40 -04:00
  • d857ff2bb7 Adjusted Fenchel's inequality. Bokuan Li 2026-06-25 12:04:16 -04:00
  • a1abb656f9 Updated convex characterisation. Bokuan Li 2026-06-25 11:44:47 -04:00
  • bc44e55e1d Renamed section. Bokuan Li 2026-06-25 11:44:36 -04:00
  • 7777095461 Added citations for elements taken from Cohn's Measure Theory. Bokuan Li 2026-06-24 23:28:30 -04:00
  • 373bc8a223 Adjusted wording in Fenchel-Moreau. Bokuan Li 2026-06-24 23:21:52 -04:00
  • e50cc6fb46 Updated gitignore. Bokuan Li 2026-06-24 23:14:50 -04:00
  • 460c84a483 Fixed up notation mistake. Bokuan Li 2026-06-24 22:36:08 -04:00
  • 177ed32433 More typo fixes. Bokuan Li 2026-06-24 22:09:17 -04:00
  • c81b77a721 Added the separable corollary to the Legendre transform. Bokuan Li 2026-06-24 22:06:22 -04:00
  • c897b3022e Fixed sign typo in Fenchel-Moreau. Bokuan Li 2026-06-24 21:55:34 -04:00
  • 81e4ef6ffe Updated notation and formulation in the Fenchel Moreau theorem. Bokuan Li 2026-06-24 21:44:58 -04:00
  • 9b6385cc16 Fixed typo in Fenchel-Moreau. Bokuan Li 2026-06-24 19:48:55 -04:00
  • 32ba2483ad Added the Legendre transform. Bokuan Li 2026-06-24 18:29:26 -04:00
  • a9890cbcab Added the subdifferential. Bokuan Li 2026-06-24 14:18:59 -04:00
  • b20ae09a0c Fixed up convention in convex functions. Bokuan Li 2026-06-24 14:18:45 -04:00
  • cddd7a4d55 Cleaned up citation stlye changes. Bokuan Li 2026-06-24 14:18:27 -04:00
  • 4764ed2fc4 Added Clarke to the list of references. Bokuan Li 2026-06-24 14:05:32 -04:00
  • c1b7a1a78e Sharpened the Hahn-Banach theorem. Bokuan Li 2026-06-24 14:05:23 -04:00
  • bbd017f76c Upgraded the separable dual lemma. Bokuan Li 2026-06-24 12:28:41 -04:00
  • eec22ac433 Minor typo in UI. Bokuan Li 2026-06-23 23:37:05 -04:00
  • 8b5da0b349 Added elementary facts about conve functions. Bokuan Li 2026-06-23 22:38:23 -04:00
  • c3751d034f Added the modular function. Bokuan Li 2026-06-23 20:18:44 -04:00
  • aa928717d0 Minor style adjustment in Urysohn. Bokuan Li 2026-06-23 19:40:45 -04:00
  • 15dec0e93f Fixed typo in LCH. Bokuan Li 2026-06-23 15:11:01 -04:00
  • ea097e46e8 Minor adjustments. Bokuan Li 2026-06-22 20:07:17 -04:00
  • adc5d1828a Fixed missing macro. Bokuan Li 2026-06-22 13:27:12 -04:00
  • 707b5310da Cleaned up convergence in measure. Bokuan Li 2026-06-22 13:18:17 -04:00
  • 05e9571794 Updated formulation of convergence in measure. Bokuan Li 2026-06-22 13:06:15 -04:00
  • 3bf3f2a85c Adjusted notation for spaces of measurable functions. Bokuan Li 2026-06-22 12:55:37 -04:00
  • b52626f3a1 Added a few points about Cauchy completeness of metric spaces. Bokuan Li 2026-06-22 12:47:25 -04:00
  • 47b8f198e1 Clamped the Ky Fan metric. Bokuan Li 2026-06-22 12:33:43 -04:00
  • 8cbd165df3 Updated main description. Bokuan Li 2026-06-21 23:28:31 -04:00
  • a6cd3c7a1b Fixed definition of LCH spaces. Bokuan Li 2026-06-21 23:26:35 -04:00
  • 3a8db01be5 Added uniform description for convergence in measure. Bokuan Li 2026-06-21 21:58:14 -04:00
  • f107df48bf MAJOR RETRACTION IN UNIFORMITY DEFINING PROPOSITION. Bokuan Li 2026-06-21 21:56:28 -04:00
  • a57686be8f Added notation for space of measurable functions. Bokuan Li 2026-06-21 21:08:13 -04:00
  • 66dd4b0068 Fixed typo in Lebesgue lemma. Bokuan Li 2026-06-21 20:53:43 -04:00
  • 84fb052c78 Fixed more typos for Scheffe. Bokuan Li 2026-06-21 00:29:02 -04:00
  • 19e2d2df51 Typo fixes in Scheffe. Bokuan Li 2026-06-21 00:24:59 -04:00
  • 8c5400bf88 Adjusted the in measure version of DCT. Bokuan Li 2026-06-21 00:22:48 -04:00
  • 5ce01bd9f3 Added draft of Scheffe's lemma. Bokuan Li 2026-06-21 00:21:11 -04:00