Commit Graph
100 Commits
Author SHA1 Message Date
Bokuan Li 754cba965b Added the Radon-Nikodym theorem for finite measures.
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2026-06-14 21:20:35 -04:00
Bokuan Li df1d959331 Added the basics of Hilbert spaces.
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2026-06-14 17:01:52 -04:00
Bokuan Li 9ec4eea839 Added the method of complex interpolation.
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2026-06-10 23:39:46 -04:00
Bokuan Li 1c211eac9a Housekeeping. 2026-06-10 15:16:43 -04:00
Bokuan Li 60c2144e9e Added a bit of interpolation spaces.
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2026-06-09 22:10:48 -04:00
Bokuan Li 4f613e6d40 Added Hadamard's Three Lines Lemma. 2026-06-09 21:00:52 -04:00
Bokuan Li 99d772d1c8 Added the Riesz decomposition.
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2026-06-05 21:57:02 -04:00
Bokuan Li 09a94756ea Added basics of C*-algebras.
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2026-06-04 17:54:06 -04:00
Bokuan Li 7ce835cef2 Added sneaky interpolation functor jokes. 2026-06-04 16:45:03 -04:00
Bokuan Li 2444406ec1 Added facts about C_0. 2026-06-04 16:31:26 -04:00
Bokuan Li 13a0e07b72 Fixed some numbering problems. 2026-06-04 13:41:05 -04:00
Bokuan Li ebead6c022 Added the unitisation. 2026-06-04 13:39:55 -04:00
Bokuan Li 6441352421 Fixed wrong proof marker.
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2026-06-03 17:24:30 -04:00
Bokuan Li 677a396e24 Fixed missing citation.
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2026-06-03 17:13:07 -04:00
Bokuan Li 6c9c479198 Adjusted prose in example facts.
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2026-06-03 17:08:55 -04:00
Bokuan Li 668679063b Added some example facts. 2026-06-03 16:56:40 -04:00
Bokuan Li f72f815c72 Added basic facts about the Gelfand transform. 2026-06-03 15:44:13 -04:00
Bokuan Li 56f3ae37f7 Slight adjustments in known results. 2026-06-03 14:37:13 -04:00
Bokuan Li 2c1169e55a Added a handful of examples.
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2026-06-02 21:39:59 -04:00
Bokuan Li 42433c40ca Upgraded prose.
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2026-06-02 20:26:07 -04:00
Bokuan Li f4bcc76bd0 Added the GKZ Theorem.
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2026-06-02 20:21:07 -04:00
Bokuan Li 54a518e9e2 Added setup for the GKZ theorem. 2026-06-02 19:11:59 -04:00
Bokuan Li 44d8bbd4da Added basic facts on maximal ideals. 2026-06-02 15:40:18 -04:00
Bokuan Li c189b7da1a Fixed typo.
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2026-06-01 23:55:52 -04:00
Bokuan Li 787f89e3a6 Fixed wrong theorem name.
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2026-06-01 17:30:38 -04:00
Bokuan Li f071a4ff31 Added lemmas on the identity component of the general linear group. 2026-06-01 17:30:03 -04:00
Bokuan Li 313f071f20 Added the spectral mapping theorem.
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2026-06-01 16:38:02 -04:00
Bokuan Li fb9febc01b Fixed typo in notations. 2026-06-01 00:05:45 -04:00
Bokuan Li 639aa253cf Slightly adjusted notation.
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2026-05-31 23:20:08 -04:00
Bokuan Li 5cf2bd9f10 Added missing assumption.
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2026-05-31 23:14:56 -04:00
Bokuan Li bfa5aee60e Added the holomorphic functional calculus.
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2026-05-31 23:12:15 -04:00
Bokuan Li 73951c9d4c Fixed typo with 1/2pi i. 2026-05-31 20:00:40 -04:00
Bokuan Li 85e73baf76 Added citation. 2026-05-31 19:30:12 -04:00
Bokuan Li 3a07b5331e Added basics of Banach algebras. 2026-05-31 19:26:20 -04:00
Bokuan Li fb8178b7ee Slight wording adjustments. 2026-05-31 15:53:32 -04:00
Bokuan Li 47145cdf58 Adjusted labeling of conditions for Banach-Steinhaus.
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2026-05-30 20:40:38 -04:00
Bokuan Li edde66facc Various typo fixes.
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2026-05-30 20:35:32 -04:00
Bokuan Li 0cea712b96 Added Runge's theorem.
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2026-05-30 20:29:17 -04:00
Bokuan Li eef9ef89b0 Added some notations. 2026-05-28 13:03:41 -04:00
Bokuan Li 1d65f25d03 Added the one-point compactification. 2026-05-28 12:55:23 -04:00
Bokuan Li 5a4c9f5d0e Updated Alaoglu's theorem.
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2026-05-27 23:53:22 -04:00
Bokuan Li 02bd8479bc Added path lemma.
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2026-05-27 22:59:06 -04:00
Bokuan Li 5923b45f9d Added Urysohn Metrisation theorem and compactness theorems.
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2026-05-26 19:32:02 -04:00
Bokuan Li f6c5976873 Fixed some typos.
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2026-05-25 21:05:21 -04:00
Bokuan Li 047ffe4472 Added the complex conjugation.
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2026-05-25 20:59:22 -04:00
Bokuan Li 65fdc1cc8d Added the Stone-Weierstrass Theorem. 2026-05-25 20:38:20 -04:00
Bokuan Li 964cb2450a Typo fix.
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2026-05-25 17:16:54 -04:00
Bokuan Li 719e9a1f7a Added complexification.
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2026-05-23 21:19:04 -04:00
Bokuan Li a058df3163 Added more complex analysis. 2026-05-18 18:06:02 -04:00
Bokuan Li 85d1d78bda Added appropriate form of Taylor's formula. 2026-05-18 16:24:43 -04:00
Bokuan Li 3a0e5cc351 Fixed typo.
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2026-05-16 21:49:56 -04:00
Bokuan Li 44d122e052 Added definition of holomorphic functions.
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2026-05-16 21:42:56 -04:00
Bokuan Li 88d71d6654 Fixed small typos. 2026-05-16 13:06:48 -04:00
Bokuan Li 365c89e773 Added Fubini for RS integrals.
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2026-05-15 20:30:20 -04:00
Bokuan Li 3a8de41020 Added the homotopic version of Cauchy's theorem. 2026-05-15 19:31:39 -04:00
Bokuan Li 6fdf6a64fd Added uniform structures for completely regular spaces. Added calculus lemma.
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2026-05-15 00:39:41 -04:00
Bokuan Li c1a9e11dbb Fixed mistakes in FTC for path integrals.
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2026-05-13 16:29:09 -04:00
Bokuan Li 9f3c8a2e81 Added remark reflecting on past mistakes. 2026-05-13 15:21:46 -04:00
Bokuan Li 06b50c9b06 Adjusted statement of FTC for path integrals.
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2026-05-11 21:22:27 -04:00
Bokuan Li a4642a0128 Added FTC for path integrals.
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2026-05-11 21:21:26 -04:00
Bokuan Li 4ba2e76b44 Added the principal logarithm. 2026-05-11 16:11:33 -04:00
Bokuan Li 538a02ba37 Added the inverse function theorem.
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2026-05-10 19:42:25 -04:00
Bokuan Li 7fdf1a8d6e Added power series.
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2026-05-09 19:57:18 -04:00
Bokuan Li 8d881dfa97 Added the bipolar theorem. 2026-05-09 18:15:10 -04:00
Bokuan Li 2e00ac6f10 Adjusted the interchange of limits and derivaties.
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2026-05-08 18:51:09 -04:00
Bokuan Li 5f50dc1157 Updated the power rule to the non-symmetric generality.
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2026-05-08 18:36:44 -04:00
Bokuan Li 248c89240b Updated notation for higher derivatives. 2026-05-08 14:17:28 -04:00
Bokuan Li 277c2e2625 Added the theorem for interchanging limits and derivatives.
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2026-05-08 01:25:39 -04:00
Bokuan Li e8474bba3e Fixed equicontinuous formulation.
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2026-05-06 23:31:25 -04:00
Bokuan Li 57c32a3c5e Updated spelling of barreled to barrelled for consistency. 2026-05-06 16:50:37 -04:00
Bokuan Li 7e6e37d3e8 Housekeeping. 2026-05-06 16:41:51 -04:00
Bokuan Li fdc5e43d82 Added the separate and joint continuity theorem.
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2026-05-06 16:31:41 -04:00
Bokuan Li 5afdc1fcb9 Adjusted wording of Banach-Steinhaus.
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2026-05-06 00:32:24 -04:00
Bokuan Li ca3465b3d4 Fixed indexing mistake in Arzela-Ascoli.
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2026-05-06 00:30:02 -04:00
Bokuan Li 07fe8b35c0 Added the Banach-Steinhaus theorem.
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2026-05-06 00:27:05 -04:00
Bokuan Li ce56f5d167 Adjusted organisation in the TVS chapter. 2026-05-05 21:58:54 -04:00
Bokuan Li 97372173e1 Fixed regex incident.
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2026-05-05 02:00:05 -04:00
Bokuan Li 0f2e69d1f9 Polished A-A and added new lines for broken enumerates.
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2026-05-05 01:50:35 -04:00
Bokuan Li 47a7e1de68 Added notes on equicontinuity.
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2026-05-05 01:10:56 -04:00
Bokuan Li 227436a9c2 Added saturated ideals. 2026-05-04 17:54:03 -04:00
Bokuan Li e3c16a98b4 Updated the notation for convex and circled hulls. 2026-05-04 17:15:54 -04:00
Bokuan Li 60115baa41 Replaced references to upward-directed families with ideals. 2026-05-04 17:08:01 -04:00
Bokuan Li e4da295fd9 Added introduction to polars. 2026-05-04 16:04:09 -04:00
Bokuan Li b2af2d8afb Fixed typo in dual systems.
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2026-05-03 22:57:48 -04:00
Bokuan Li ca5e81fdbc Started duality.
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2026-05-03 22:49:27 -04:00
Bokuan Li ba5830d5b6 Added associated space notation.
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2026-05-02 16:00:33 -04:00
Bokuan Li 1e53581113 Added bornological spaces. 2026-05-02 15:59:03 -04:00
Bokuan Li dcf11fb978 Added more bits on bornologic spaces.
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2026-05-01 19:27:38 -04:00
Bokuan Li 0ef220bba5 Added proof for the BV claim. 2026-05-01 18:33:10 -04:00
Bokuan Li 4e0efaf7f5 Adjusted formulation of a total variation statement. 2026-05-01 18:31:08 -04:00
Bokuan Li 10e520dff3 Updated formulation in BV.
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2026-05-01 16:40:01 -04:00
Bokuan Li 2219ce0b15 Added barreled spaces.
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2026-05-01 16:27:14 -04:00
Bokuan Li 3077563278 Used "separated" instead of Hausdorff in the context of topological vector spaces. 2026-05-01 13:32:08 -04:00
Bokuan Li caf7790b15 Fixed typo in Cauchy in measure. 2026-05-01 13:29:36 -04:00
Bokuan Li 95829261c7 Fixed typo in FTC for Riemann integrals.
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2026-04-28 18:09:27 -04:00
Bokuan Li 225794ff81 Fixed typo in the definition of regulated maps.
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2026-04-28 18:07:27 -04:00
Bokuan Li 6a960a6231 Fixed typo in variation function.
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2026-04-28 18:05:37 -04:00
Bokuan Li d187feb618 Fixed partition index typo. 2026-04-28 18:04:05 -04:00
Bokuan Li 34736f99a8 More typo fixes.
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2026-04-28 14:34:44 -04:00
Bokuan Li d80fae112d Fixed more convex typos. 2026-04-28 14:27:23 -04:00