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  • 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
  • bfa5aee60e Added the holomorphic functional calculus. Bokuan Li 2026-05-31 23:12:15 -04:00
  • 73951c9d4c Fixed typo with 1/2pi i. Bokuan Li 2026-05-31 20:00:40 -04:00
  • 85e73baf76 Added citation. Bokuan Li 2026-05-31 19:30:12 -04:00
  • 3a07b5331e Added basics of Banach algebras. Bokuan Li 2026-05-31 19:26:20 -04:00
  • fb8178b7ee Slight wording adjustments. Bokuan Li 2026-05-31 15:53:32 -04:00
  • 47145cdf58 Adjusted labeling of conditions for Banach-Steinhaus. Bokuan Li 2026-05-30 20:40:38 -04:00
  • edde66facc Various typo fixes. Bokuan Li 2026-05-30 20:35:32 -04:00
  • 0cea712b96 Added Runge's theorem. Bokuan Li 2026-05-30 20:29:17 -04:00
  • eef9ef89b0 Added some notations. Bokuan Li 2026-05-28 13:03:41 -04:00
  • 1d65f25d03 Added the one-point compactification. Bokuan Li 2026-05-28 12:55:23 -04:00
  • 5a4c9f5d0e Updated Alaoglu's theorem. Bokuan Li 2026-05-27 23:53:22 -04:00
  • 02bd8479bc Added path lemma. Bokuan Li 2026-05-27 22:59:06 -04:00
  • 5923b45f9d Added Urysohn Metrisation theorem and compactness theorems. Bokuan Li 2026-05-26 19:32:02 -04:00
  • f6c5976873 Fixed some typos. Bokuan Li 2026-05-25 21:05:21 -04:00
  • 047ffe4472 Added the complex conjugation. Bokuan Li 2026-05-25 20:59:22 -04:00
  • 65fdc1cc8d Added the Stone-Weierstrass Theorem. Bokuan Li 2026-05-25 20:38:20 -04:00
  • 964cb2450a Typo fix. Bokuan Li 2026-05-25 17:16:54 -04:00
  • 719e9a1f7a Added complexification. Bokuan Li 2026-05-23 21:19:04 -04:00
  • a058df3163 Added more complex analysis. Bokuan Li 2026-05-18 18:06:02 -04:00
  • 85d1d78bda Added appropriate form of Taylor's formula. Bokuan Li 2026-05-18 16:24:43 -04:00
  • 3a0e5cc351 Fixed typo. Bokuan Li 2026-05-16 21:49:56 -04:00
  • 44d122e052 Added definition of holomorphic functions. Bokuan Li 2026-05-16 21:42:56 -04:00
  • 88d71d6654 Fixed small typos. Bokuan Li 2026-05-16 13:06:48 -04:00
  • 365c89e773 Added Fubini for RS integrals. Bokuan Li 2026-05-15 20:30:20 -04:00
  • 3a8de41020 Added the homotopic version of Cauchy's theorem. Bokuan Li 2026-05-15 19:31:39 -04:00