[數撚圍爐區] 將一個波分成五份, 然後砌兩個同原本一樣的波的鬼故事 (108)

其實我反而擅長做algebra多過analysis，Lang’s proof冇寫得好explicit嘅部分我會識fill in，有啲題目我係識做，但analysis係一頭霧水

Algebra只需要俾啲hint我就識 Analysis係真係好弱雞

調返轉我擅長做analysis多過algebra

analysis一開始知點construct同控制number existence就得，algebra相對少呢d

其實都ok嘅，除非係好奇奇怪怪嘅function，咁我就真係呆咗

奇怪既function通常難去construct到d嘢，但係又唔知點解construct到同fix到d point同neighborhood又覺得有滿足感

Not me

sad
Analysis係我覺得最有趣既嘢

用result去證particular function有時可以
例如當我證sin x嘅power series係點converge on radius of convergence(其實就係成條實數線），點differentiable on radius of convergence，有種construct sin x嘅感覺，我唔再從三角形呢啲geometric直觀嘅概念去理解，而係用algebraic同logic嘅definition去理解佢

sin x既construction可以用properties去develop到sine function.如果係measure theory既世界既話，奇怪既function都可以construct到

唔識measure theory

好慘measure theory係analysis最基礎既嘢

Measure theory我自己最有印象嘅係證f is integratable iff set of discontinuous point being measure 0，同埋小部份probability space

其實我上analysis係為analytic continuation
就係嗰個1+2+3+…=-1/12
但係依家都仲未識

但數學嘅嘢已經完成咗一半，Galois已完

但你唔好叫我reproduce嗰proof出嚟 我做唔到

已拿下半壁江山

做咗啲exercise我要休息一陣
一兩個月後就上analysis

如果完埋analytic continuation，咁我或者會繼續研究數學嘅，但就冇乜嘢大目標

仲有 我聽講過一啲概念講咩叫essential supremum同infirmum，除咗某幾個點之外，佢係sup/inf almost everywhere，我覺得幾有趣。但係可惜我對呢啲概念只有表面上嘅認識

同埋（我唔知啱唔啱）lebesgue integral就係動用埋codomain去做partition，唔似riemann integral咁只係喺domain做partition

因為Lebesgue integral 個codomain map返去domain唔知會出咩set，所以Lebesgue integral通常都要考慮map返既set究竟係唔係measurable

最有趣個part通常係essential supremum ，因為數學家用essential supremum define既L-inf space通常都會用嚟證uniform convergence almost everywhere 只要error estimate 係L-inf space就得

f is Riemann integratable iff f is bounded and the set of discontinuous point is of measure 0

就咁講integrable可以係Lebgesue integrable

general measure space個domain邊有interval比你

多謝更正，我都係憑印象諗下我有冇學過同measure theory相關嘅概念