【正文】 s to e and recapping the key points. This device, not used in the original, is culturally understandable but artistically mediocre. What puzzles me is the two new songs for the opening and end credits. They were written in English, but sung by Chinese with an unfortable accent. They were obviously designed to appeal to an Englishspeaking base, but do not jibe with the Chinese dialogue. Speaking of the dialogue, the English translation, picked apart by some Chinese, is too literal for my taste. I can imagine a typical American hit by a flurry of royal ranks, addresses and g。s cultural foray overseas, has been widely panned by its home audience. Retitled Empresses in the Palace, the American version has been shortened from its original 76 episodes at 45 minutes each, to six 90minute episodes. The quick pacing threw off many native viewers, who are accustomed to a more leisurely daytimesoapstyle narrative rhythm. (Chinese TV stations would run two or three episodes every day.) I did not finish the fulllength version and found the truncated one not difficult to follow. What39。s president, who is also a renowned tenor, tells China Daily. During a tour in 1985, he went to a village and met an elderly local man, who told him a story about his friendship with a solider from Shenyang, capital of Northeast China39。s villages and entertain nomadic families, but their fame has s pread around the world. On May 16 and 17, nearly 100 singers and dancers from the troupe performed at Beijing39。t just about sharing art with nomadic families but also about gaining inspiration for the music and dance. Ulan Muqir literally translates as red burgeon, and today39。t help but sing the folk songs, Nasun says. The vastness of Inner Mongolia and the lack of entertainment options for people living there, made their lives lonely. The nomadic people were very excited about our visits, Nasun recalls. We didn39。s Zhangye city during their journey to Kazakhstan, May 5, 2021. The caravan, consisting of more than 100 camels, three horsedrawn carriages and four support vehicles, started the trip from Jingyang county in Shaanxi on Sept 19, 2021. It will pass through Gansu province and Xinjiang Uygur autonomous region, and finally arrive in Almaty, formerly known as AlmaAta, the largest city in Kazakhstan, and Dungan in Zhambyl province. The trip will cover about 15,000 kilometers and take the caravan more than one year to plete. The caravan is expected to return to Jingyang in March 2021. Then they will e back, carrying specialty products from Kazakhstan A small art troupe founded six decades ago has grown into a household name in the Inner Mongolia autonomous region. In the 1950s, Ulan Muqir Art Troupe was created by nine young musicians, who toured remote villages on horses and performed traditional Mongolian music and dances for nomadic families. The 54yearold was born in Tongliao, in eastern Inner Mongolia and joined the troupe in says there are 74 branch troupes across Inner Mongolia and actors give around 100 shows every year to local nomadic people. I can still recall the days when I toured with the troupe in the early 39。 18 參考文獻 [1]韋玉程 .對實分析的幾點認識 [J].河池學院學報， 2021（ 5） . [2]趙煥光 .浸透在實變函數論中的主要數學思想方法 [J].溫州師范學院學報， 1998（ 6） . [3]鐘寶東 .試論逐次逼近法 [J].曲阜師范大學學報， 1990（ 1） . [4]張慶水 .談談逐次逼近法 [J].曲阜師范學院學報， 1980（ 2） . [5]常庚哲，史濟懷 .數學分析教程 [M].北京：高等教育出版社， 2021： 195 [6]華東師范大學數學系 .數學分析（第三版） [M].北京：高等 教育出版社， 2021： 138 [7]邢家省 ， 李占現 ， 李爭輝 .可積函數的逼近性質的證明及其應用 [J].河南科學， 2021（ 6） . [8]周會會 .可積函數的判別及逼近性質的證明 [J].中國科教創(chuàng)新導刊， 2021（ 11） . [9]周民強 .實變函數論 [M].北京：北京大學出版社， 2021： 108 [10]何穗，劉敏思，喻小培 .實變函數 [M].北京：科學出版社， 2021： 79， 98 [11]江澤堅，吳智泉，紀友清 . 實變函數論（第三版） [M].北京：高等教育出版社， 2021： 111 19 為你提供優(yōu)秀的畢業(yè)論文參 考資料，請您刪除以下內容， O(∩ _∩ )O 謝謝！?。?A large group of tea merchants on camels and horses from Northwest China39。導師的博聞強識，對待科學的嚴謹態(tài)度及嚴格要求自己的態(tài)度深深地感染了我，使我受益匪淺。 因為有了你們，讓我學會了面對任何新領域，都對自己滿懷信心，堅定自己一定可以做得很出色；因為有了你們，讓我感染了老師們求學態(tài)度嚴謹和思考問題的方式；因為有了你們，讓我感受到數學的抽象美等等。 17 致謝 四年的學習即將畫上圓滿的句號，四年的時間很漫長，但是有了和藹可親師長的陪伴，有了朋友們的互相幫助，四年時間變得很短，讓我過得充實多彩！在此衷心感謝大學四年來所有的任課教師， 特別是教授我們函數論課程的羅小兵老師，正是得益于他高瞻遠矚、嚴謹求實的課堂教學，我才能打下寫好本課題所必需的堅實的理論基礎 。 在R 積分方面，用連續(xù)函數序列逼近 R 可積函數；在 L 積分方面，有類似的結論，用連續(xù)函數序列逼近可測函數。 在 R 積分方面，用階梯函數來逼近閉區(qū)間 R 可積函數；在 L 積分方面，用簡單函數來逼近可測函數，又階梯函數可以看做簡單函數在一維空間上的特例，后一個結論在一維空間下推廣了前一個結論。 16 此定理說明 L可積函數可由連續(xù)函數逼近。 于是 ( ) ( ) d ( ) ( ) d ( ) ( ) dNNE E E Ef x g x x f x g x x f x g x x?? ? ? ? ?? ? ? ( ) d ( ) d ( ) ( ) dN N N NE E E E Ff x x g x x f x g x x??? ? ? ?? ? ? ? ?24N N NN m E N m E E F?? ? ? ? ? 442??? ?? ? ? ? 。由積分的絕對連續(xù)性， 對任意 0?? ，存在 1N? ，使 ( ) d 4NN ENm E f x x???? 。 又 mE??? ,由單調可測集列性質，則 l im 。 ( )nE x f x E x f x n??? ? ? ? ? ? ? ? ?? ? ? ?，記 。 又1。 [10] 證明 因為 ()fx在 E 上的 L可積，則 ()fx在 E 上幾乎處處有限，即 。 從 定義 5可以看出，非負可測函數的 L積分可由有界函數的 L積分來逼近。 ? ?( ) dn nE f x x? 單調遞增且有界，這是因為 1nnEE?? ， ? ? ? ? 1( ) ( )nnf x f x ?? ，則 ? ? ? ? ? ?11 1( ) d ( ) d ( ) dn n nnnnE E Ef x x f x x f x x?? ?? ? ? ? ?? ? ?， 于是 ? ?lim ( ) dn nEn f x x???存在。即對于任意正整數 n ，都有 1( ) ( )nnf x f x?? ，那么 ? ?lim ( )nn fx??存在，下證 ? ? ? ?lim ( )nn f x f x?? ?。 15 顯然截斷函數列中每個函數 ??nfx為有界函數。 從而任何可測集 E 都可以表示為一列單調遞增有界可測集 mE 的極限。即 ? ?mE 為單調遞增可測列。 又 1mmKK? ? ，則 1mmEE? ? 。 證明 作閉矩體 ? ?? ?12, , , 。 用有界函數的 L積分逼近無界函數的 L積分 設 ()fx在 E 上非負有界且 mE??? ，當 E 為區(qū)間， ()fx在 E 上的 L積分與 R積分在形式上相同，現在設 nE?R 是任一可測集， ()fx在 E 上非負可測，考慮 ()fx在 E 上的 L積分。即 ? ?lim ( ), . .nn x f x a e??? ? 于 E 。由 例 4可知， ??nF 是單調遞增，記1 nnFF???,則對任意 xF? ,存在 N ,使當 nN? 時， nxF? ，于是 ( ) ( )x f x? ? ，所以 ? ?lim ( )nn x f x??? ?， ? ?xF? 。 證明 ? ?lim ( ),