[數學普及] Measure Theory (測度論) 簡介 ver. 2

Elias 2017-12-25 02:26:32 唔知咩時候會講下

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但呢度唔會講住，用個比較intuitive的方法講左先

Elias 2017-12-25 15:06:06 pish

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CSniper 2017-12-25 17:40:48 樓主真Chur
不過個post又令我想拎番以前讀 analysis （CUHK MATH 2050 2060）啲野出黎睇
支持高汁post

Elias 2017-12-26 06:57:52 呢個應該係 4050

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CSniper 2017-12-26 11:53:07 我果陣無到咁深
（我minor 黎架炸唔係major 唔敢挑戰 real 同 functional）

Elias 2017-12-26 12:48:28 Functiomal 無咁多 epsilon delta 會開心d
同埋functional 需要linear algebra 同 point set topology 多過 elementary analysis

Elias 2017-12-26 12:49:29

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Elias 2017-12-26 13:23:16

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Elias 2017-12-27 17:13:51 https://lihkgmeasure.wordpress.com/2017/12/26/recommended-pure-mathematics-textbooks-for-undergraduates/
有興趣可以望下 (未完成)

RVZ01 2017-12-27 17:53:14 請問係咪non-continuous function 係咪搵唔到area?
指緊non-continuous 既interval

狐狸叔叔 2017-12-27 20:39:02 好似唔係，只要discontinuous既點足夠少就係riemann integrable
利申：唔識

日向葵海（主唱） 2017-12-27 20:40:36 Iff set of discontinuity is countable

Elias 2017-12-27 23:11:58 Set of continuity is of length zero
Countable set 只係 length zero ge 特例
Cantor set 係length zero 但 uncountable

Elias 2017-12-27 23:13:46 唔係呀，我一開講Riemann integral 果陣個d estimation 用ge function咪discontinuous lor

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Elias 2017-12-27 23:14:16

請問係咪non-continuous function 係咪搵唔到area?
指緊non-continuous 既interval
好似唔係，只要discontinuous既點足夠少就係riemann integrable
利申：唔識
Iff set of discontinuity is countable
Set of discontinuity is of length zero
Countable set 只係 length zero ge 特例
Cantor set 係length zero 但 uncountable

日向葵海（主唱） 2017-12-27 23:24:30 記錯咗

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Elias 2017-12-27 23:30:24 諗住砍掉重練

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Elias 2017-12-27 23:37:13 其實no one cares 呢條theorem
用處唔大，呢條theorem 只係話太多discontinuities 會令Riemann integral 條橋行唔通
但唔代表用Lebesgue 條橋唔得
有條定理就係話Riemann integrable implies Lebesgue integrable.

狐狸叔叔 2017-12-28 18:30:59 又砍？諗住點重練？

Elias 2017-12-30 08:46:23 諗下有無D咩 intuitive的方法講, 而家太 technical, technical ge部份不如留返比D真係有興趣的人搵本書睇