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55bd2e48594ca381b3d12523513a35a1c1c823d5
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Bokuan Li
55bd2e4859 Fixed typo.
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2026-06-27 22:41:48 -04:00
Bokuan Li
d8f56ef537 RETRACTION: SEPARABILITY REQUIRED TO DEFINE CONVERGENCE IN MEASURE 2026-06-27 22:38:39 -04:00
Bokuan Li
ce52ac4b63 Edited the open preimage functions. 2026-06-27 22:35:32 -04:00
Bokuan Li
4616ac2861 First draft for open preimage functions. 2026-06-27 22:06:50 -04:00
Bokuan Li
80f79fb30d Added preimage functions. 2026-06-27 18:41:06 -04:00
Bokuan Li
48a0e63f61 Added elementary facts about localisable measure spaces. 2026-06-27 17:11:57 -04:00
Bokuan Li
3d9c47bda1 Minor housekeeping. 2026-06-27 14:12:40 -04:00
Bokuan Li
968fbe6eba Added the support function.
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2026-06-27 13:17:45 -04:00
Bokuan Li
eed3a342e4 Typo fixes.
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2026-06-26 12:59:13 -04:00
Bokuan Li
369a1e72db Adjustment in Fenchl-Moreau. 2026-06-26 12:57:30 -04:00
Bokuan Li
03e7899904 Added the Mackey-Arens theorem (for real).
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2026-06-26 00:45:59 -04:00
Bokuan Li
fbdf280f11 Fixed gap in maximum modulus strip. 2026-06-26 00:44:31 -04:00
Bokuan Li
91752ee561 Added compact definition.
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2026-06-26 00:17:28 -04:00
Bokuan Li
9c08e0a525 Added the Mackey-Arens theorem. 2026-06-26 00:16:36 -04:00
Bokuan Li
061a4f3034 More prose corrections.
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2026-06-25 19:22:37 -04:00
Bokuan Li
98f96b2af1 Performed more housekeeping for the Legendre transform.
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2026-06-25 19:16:16 -04:00
Bokuan Li
4b404d40a6 Updated the A-A theorem to include convergence on a dense subset.
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2026-06-25 13:58:38 -04:00
Bokuan Li
b7f93c1110 Updated the legendre corollary.
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2026-06-25 13:32:44 -04:00
Bokuan Li
2c4a8c9d22 Typo fixes for the separable dual lemma.
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2026-06-25 13:17:05 -04:00
Bokuan Li
83072f4ba4 Adjusted the Legendre sectoin.
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2026-06-25 13:03:51 -04:00
Bokuan Li
c19aaf7fe3 Fixed infinity problem. 2026-06-25 12:23:40 -04:00
Bokuan Li
d857ff2bb7 Adjusted Fenchel's inequality. 2026-06-25 12:04:16 -04:00
Bokuan Li
a1abb656f9 Updated convex characterisation. 2026-06-25 11:44:47 -04:00
Bokuan Li
bc44e55e1d Renamed section. 2026-06-25 11:44:36 -04:00
Bokuan Li
7777095461 Added citations for elements taken from Cohn's Measure Theory.
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2026-06-24 23:28:30 -04:00
Bokuan Li
373bc8a223 Adjusted wording in Fenchel-Moreau.
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2026-06-24 23:21:52 -04:00
Bokuan Li
e50cc6fb46 Updated gitignore. 2026-06-24 23:14:50 -04:00
Bokuan Li
460c84a483 Fixed up notation mistake.
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2026-06-24 22:36:08 -04:00
Bokuan Li
177ed32433 More typo fixes.
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2026-06-24 22:09:17 -04:00
Bokuan Li
c81b77a721 Added the separable corollary to the Legendre transform.
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2026-06-24 22:06:22 -04:00
Bokuan Li
c897b3022e Fixed sign typo in Fenchel-Moreau.
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2026-06-24 21:55:34 -04:00
Bokuan Li
81e4ef6ffe Updated notation and formulation in the Fenchel Moreau theorem.
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2026-06-24 21:44:58 -04:00
Bokuan Li
9b6385cc16 Fixed typo in Fenchel-Moreau.
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2026-06-24 19:48:55 -04:00
Bokuan Li
32ba2483ad Added the Legendre transform.
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2026-06-24 18:29:26 -04:00
Bokuan Li
a9890cbcab Added the subdifferential. 2026-06-24 14:18:59 -04:00
Bokuan Li
b20ae09a0c Fixed up convention in convex functions. 2026-06-24 14:18:45 -04:00
Bokuan Li
cddd7a4d55 Cleaned up citation stlye changes. 2026-06-24 14:18:27 -04:00
Bokuan Li
4764ed2fc4 Added Clarke to the list of references. 2026-06-24 14:05:32 -04:00
Bokuan Li
c1b7a1a78e Sharpened the Hahn-Banach theorem. 2026-06-24 14:05:23 -04:00
Bokuan Li
bbd017f76c Upgraded the separable dual lemma. 2026-06-24 12:28:41 -04:00
Bokuan Li
eec22ac433 Minor typo in UI.
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2026-06-23 23:37:05 -04:00
Bokuan Li
8b5da0b349 Added elementary facts about conve functions.
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2026-06-23 22:38:23 -04:00
Bokuan Li
c3751d034f Added the modular function.
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2026-06-23 20:18:44 -04:00
Bokuan Li
aa928717d0 Minor style adjustment in Urysohn. 2026-06-23 19:40:45 -04:00
Bokuan Li
15dec0e93f Fixed typo in LCH.
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2026-06-23 15:11:01 -04:00
Bokuan Li
ea097e46e8 Minor adjustments. 2026-06-22 20:07:17 -04:00
Bokuan Li
adc5d1828a Fixed missing macro.
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2026-06-22 13:27:12 -04:00
Bokuan Li
707b5310da Cleaned up convergence in measure.
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2026-06-22 13:18:17 -04:00
Bokuan Li
05e9571794 Updated formulation of convergence in measure.
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2026-06-22 13:06:15 -04:00
Bokuan Li
3bf3f2a85c Adjusted notation for spaces of measurable functions. 2026-06-22 12:55:37 -04:00