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  • 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
  • 15fc3f430b Slight adjustments. Bokuan Li 2026-06-20 21:29:53 -04:00
  • 10c6215427 Added a local to global characterisation of convergence in measure. Bokuan Li 2026-06-20 20:45:36 -04:00
  • 1026ff782e Adjusted some things in Radon meaasures. Bokuan Li 2026-06-20 20:45:20 -04:00
  • 9227565f21 Added translation properties for Haar. Bokuan Li 2026-06-20 10:28:50 -04:00
  • ea091f006a Adjusted wording in Haar. Bokuan Li 2026-06-20 10:13:19 -04:00
  • 094320ef29 Cleaned up MCT in measure. Bokuan Li 2026-06-20 10:11:25 -04:00
  • 242c7ebea1 Updated the Lebesgue non-negative integral formula. Bokuan Li 2026-06-20 09:48:01 -04:00
  • 9dae6324ef Updated remark for dominated convergence. Bokuan Li 2026-06-19 20:54:43 -04:00
  • 2d75e7c029 Added MCT for convergence in measure. Bokuan Li 2026-06-19 20:50:42 -04:00
  • 8742c4f7cd Added MCT for convergence in measure. Bokuan Li 2026-06-19 20:34:15 -04:00
  • dc789884bc Typo. Bokuan Li 2026-06-19 17:42:31 -04:00
  • 1722ddb933 Added the Vitali convergence theorem. Bokuan Li 2026-06-19 17:36:53 -04:00
  • a97be99b8a Fixed typos in the haar proof. Bokuan Li 2026-06-19 13:01:06 -04:00
  • 64788a5322 Added a variation bound for scalar measures. Bokuan Li 2026-06-19 12:59:33 -04:00
  • 9504125410 Added uniqueness of Haar. Bokuan Li 2026-06-18 21:00:12 -04:00
  • 6487655eb3 Fixed typo. Bokuan Li 2026-06-18 20:21:58 -04:00
  • b68c050225 Mised 3 factor. Bokuan Li 2026-06-17 23:50:56 -04:00
  • 346b0bdfd2 Made more room. Bokuan Li 2026-06-17 23:49:24 -04:00
  • a8eed2a9ba ACTUALLY added the Haar measure. Bokuan Li 2026-06-17 23:46:13 -04:00
  • 7a678b9efe Added existence of the Haar measure. Bokuan Li 2026-06-17 23:44:23 -04:00
  • 4028f13e04 Added more facts about topological groups. Bokuan Li 2026-06-17 20:27:35 -04:00
  • 50d4a326db Slight adjustment to topological groups. Bokuan Li 2026-06-17 17:53:04 -04:00
  • f29c3cdeb7 More typo fixes. Bokuan Li 2026-06-17 17:21:36 -04:00
  • 66d4a9ef3e Funny typo. Bokuan Li 2026-06-17 17:19:35 -04:00
  • 6d84f0ea47 Performed housekeeping for topological groups. Bokuan Li 2026-06-17 17:17:37 -04:00
  • 597a92b006 Adjusted wording for the sequential statement. Bokuan Li 2026-06-16 21:09:48 -04:00
  • ff2218c79b Fixed stack exchange citation. Bokuan Li 2026-06-16 15:17:37 -04:00
  • d5d03954df Slight typographic adjustment. Bokuan Li 2026-06-16 13:45:06 -04:00
  • c31994b247 Fixed awkward phrasing. Bokuan Li 2026-06-16 13:43:42 -04:00
  • 76107709a8 Added a description of weak-* convergence in the case of bounded Borel functions. Bokuan Li 2026-06-16 13:42:54 -04:00
  • f456f79891 Fleshed out the dual of measure spaces. Bokuan Li 2026-06-16 13:25:40 -04:00
  • 07d8419fe0 Added duality result for spaces of measures. Bokuan Li 2026-06-16 13:10:24 -04:00
  • 845e616453 Fixed typos in the sequence space duality result. Bokuan Li 2026-06-16 12:35:36 -04:00
  • 49e4e15649 Added duality for the sequence spaces. Bokuan Li 2026-06-16 12:23:51 -04:00
  • b9d67bfb82 Added mental gymnastics for lp direct sums. Bokuan Li 2026-06-15 22:52:25 -04:00
  • 6c6522a1de Added l^p sequence spaces. Bokuan Li 2026-06-15 21:57:37 -04:00
  • dadddc4663 Added section regarding the duality of L^p spaces. Bokuan Li 2026-06-15 21:47:49 -04:00
  • 35efec2d90 Updated the separable dual proposition. Bokuan Li 2026-06-15 14:16:32 -04:00
  • 9f05b9dabd Fixed a handful of typos. Bokuan Li 2026-06-15 00:17:03 -04:00
  • 5b1e0f86e6 Added missing justification. Bokuan Li 2026-06-14 23:09:35 -04:00
  • 33c6a6775d Fixed typos. Bokuan Li 2026-06-14 22:59:26 -04:00
  • b2ef9f2736 Added the Vitali-Hahn-Saks theorem. Bokuan Li 2026-06-14 22:55:23 -04:00
  • 1ec807a9ca Removed pretentiousness. Bokuan Li 2026-06-14 21:29:15 -04:00
  • 16baef24e7 Oxford? comma. Bokuan Li 2026-06-14 21:26:17 -04:00
  • b8df875d0f Actually added the Radon-Nikodym theorem. Bokuan Li 2026-06-14 21:24:26 -04:00
  • 754cba965b Added the Radon-Nikodym theorem for finite measures. Bokuan Li 2026-06-14 21:20:35 -04:00
  • df1d959331 Added the basics of Hilbert spaces. Bokuan Li 2026-06-14 17:01:52 -04:00
  • 9ec4eea839 Added the method of complex interpolation. Bokuan Li 2026-06-10 23:39:46 -04:00
  • 1c211eac9a Housekeeping. Bokuan Li 2026-06-10 15:16:43 -04:00
  • 60c2144e9e Added a bit of interpolation spaces. Bokuan Li 2026-06-09 22:10:48 -04:00
  • 4f613e6d40 Added Hadamard's Three Lines Lemma. Bokuan Li 2026-06-09 21:00:52 -04:00
  • 99d772d1c8 Added the Riesz decomposition. Bokuan Li 2026-06-05 21:57:02 -04:00
  • 09a94756ea Added basics of C*-algebras. Bokuan Li 2026-06-04 17:54:06 -04:00
  • 7ce835cef2 Added sneaky interpolation functor jokes. Bokuan Li 2026-06-04 16:45:03 -04:00
  • 2444406ec1 Added facts about C_0. Bokuan Li 2026-06-04 16:31:26 -04:00
  • 13a0e07b72 Fixed some numbering problems. Bokuan Li 2026-06-04 13:41:05 -04:00
  • ebead6c022 Added the unitisation. Bokuan Li 2026-06-04 13:39:55 -04:00
  • 6441352421 Fixed wrong proof marker. Bokuan Li 2026-06-03 17:24:30 -04:00
  • 677a396e24 Fixed missing citation. Bokuan Li 2026-06-03 17:13:07 -04:00
  • 6c9c479198 Adjusted prose in example facts. Bokuan Li 2026-06-03 17:08:55 -04:00
  • 668679063b Added some example facts. Bokuan Li 2026-06-03 16:56:40 -04:00
  • f72f815c72 Added basic facts about the Gelfand transform. Bokuan Li 2026-06-03 15:44:13 -04:00
  • 56f3ae37f7 Slight adjustments in known results. Bokuan Li 2026-06-03 14:37:13 -04:00
  • 2c1169e55a Added a handful of examples. Bokuan Li 2026-06-02 21:39:59 -04:00
  • 42433c40ca Upgraded prose. Bokuan Li 2026-06-02 20:26:07 -04:00
  • f4bcc76bd0 Added the GKZ Theorem. Bokuan Li 2026-06-02 20:21:07 -04:00
  • 54a518e9e2 Added setup for the GKZ theorem. Bokuan Li 2026-06-02 19:11:59 -04:00
  • 44d8bbd4da Added basic facts on maximal ideals. Bokuan Li 2026-06-02 15:40:18 -04:00
  • c189b7da1a Fixed typo. Bokuan Li 2026-06-01 23:55:52 -04:00
  • 787f89e3a6 Fixed wrong theorem name. Bokuan Li 2026-06-01 17:30:38 -04:00
  • f071a4ff31 Added lemmas on the identity component of the general linear group. Bokuan Li 2026-06-01 17:30:03 -04:00
  • 313f071f20 Added the spectral mapping theorem. Bokuan Li 2026-06-01 16:38:02 -04:00
  • fb9febc01b Fixed typo in notations. Bokuan Li 2026-06-01 00:05:45 -04:00
  • 639aa253cf Slightly adjusted notation. Bokuan Li 2026-05-31 23:20:08 -04:00
  • 5cf2bd9f10 Added missing assumption. Bokuan Li 2026-05-31 23:14:56 -04:00