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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�(gu贸)400澶氭墍楂樼瓑闄㈡牎鎷涙敹纰╁＋銆佸崥澹爺绌剁敓鍏ュ(xu茅)鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗�锛岄儴鍒嗗(xu茅)鏍℃洿鏂拌嚦2012骞�锛�2013骞�锛涘潎鎻愪緵鏀惰不(f猫i)涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛�(di菐n)鎿娾€�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛�(di菐n)鎿娾€�鑰冨崥瑭﹀嵎搴�(k霉)鈥� 涓嬭級
澶ч€ｆ捣浜嬪ぇ瀛�(xu茅)纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冪爺澶х侗
鑰冭│绉戠洰锛氬(sh铆)璁婂嚱鏁�(sh霉)
瑭﹀嵎婊垮垎鍙婅€冭│鏅�(sh铆)闁擄細瑭﹀嵎婊垮垎鐐� 100 鍒�锛岃€冭│鏅�(sh铆)闁撶偤 180 鍒嗛悩銆�
鑰冭│鍏�(n猫i)瀹�
涓€銆� 闆嗗悎璜栧熀绀�(ch菙)
1. 闆嗗悎鍙婂叾閬�(y霉n)绠楋紱
2. 闆嗗悎鐨勫熀鏁�(sh霉)锛�
3. 鍙暩(sh霉)闆嗚垏涓嶅彲鏁�(sh霉)闆嗐€�
浜�銆� Rn
涓殑鎷�?f霉)?br/>1. 闁�(k膩i)闆嗚垏闁夐泦锛屽収(n猫i)榛�(di菐n)锛岃仛榛�(di菐n)锛屽皫(d菐o)闆�锛岄枆鍖� 锛�
2. 闁�(k膩i)闆嗙殑妲�(g貌u)閫犲畾鐞�锛�
3. 搴锋墭锛圕antor锛変笁鍒嗛泦锛屽畬鍌欓泦锛岀枏鏈楅泦锛岀瀵嗛泦锛岀穵鑷撮泦銆�
涓�銆� 娓�(c猫)搴︾悊璜�
1. 澶栨脯(c猫)搴︾殑姒傚康鍜屽熀鏈€ц唱(zh矛)锛�
2. Lebesgue 鍙脯(c猫)闆嗙殑姒傚康鑸� Caratheodory 姊濅欢锛�
3. Lebesgue 鍙脯(c猫)闆嗗叏楂�?鐨勫悇绋暣楂旀€ц唱(zh矛)锛堝鍙垪鍙姞鎬х瓑锛�锛�
4. 涓嶅彲娓�(c猫)闆嗙殑妲�(g貌u)閫狅紱
5. Lebesgue 鍙脯(c猫)闆嗙殑绛夊児(ji脿)姒傚康锛�
6. 浠ｆ暩(sh霉)锛�?浠ｆ暩(sh霉)锛孊orel 闆�銆�
鍥�銆� 鍙脯(c猫)鍑芥暩(sh霉)
1. 鍙脯(c猫)鍑芥暩(sh霉)鍙婂叾鎬ц唱(zh矛)锛�
2. 娓�(c猫)鍑芥暩(sh霉)鍒楃殑閫愰粸(di菐n)鏀舵杺銆佽繎涓€鑷存敹鏂�銆佷緷娓�(c猫)搴︽敹鏂�锛�
3. 鐢ㄩ€ｇ簩(x霉)鍑芥暩(sh霉)閫艰繎鍙脯(c猫)鍑芥暩(sh霉)锛岄閲戯紙Lusin锛夊畾鐞嗐€�
浜�銆� Lebesgue 绌嶅垎
1. Lebesgue 绌嶅垎鐨勫畾缇╄垏鎬ц唱(zh矛)锛�
2. 鍙脯(c猫)鍑芥暩(sh霉)鍒楃⿳鍒嗘敹鏂傚畾鐞�锛孡ebesgue 绌嶅垎鐨勭禃灏�(du矛)閫ｇ簩(x霉)鎬э紱
3. Lebesgue 绌嶅垎鑸� Riemman 绌嶅垎鐨勯棞(gu膩n)绯�锛�
4. 閲嶇⿳鍒�銆佺疮娆＄⿳鍒�銆丗ubini 瀹氱悊锛�
5. 鏈夌晫璁婂樊鍑芥暩(sh霉)锛岀禃灏�(du矛)閫ｇ簩(x霉)鍑芥暩(sh霉)锛孡ebesgue-Stieltjes 绌嶅垎銆�
鍩烘湰瑕佹眰
涓€銆� 闆嗗悎璜栧熀绀�(ch菙)
1. 鐔熺反鎺屾彙 闆嗗悎鍚勭ó閬�(y霉n)绠楋紙鍖呮嫭闆嗗悎鍒楃殑涓�銆佷笅妤甸檺闆嗭級锛�
2. 鐞嗚В闆嗗悎鍩烘暩(sh霉)銆佸彲鏁�(sh霉)闆嗚垏涓嶅彲鏁�(sh霉)闆嗙瓑姒傚康锛岀啛绶存帉鎻￠泦鍚堝熀鏁�(sh霉)鐨�
姣旇純鍜岃▓(j矛)绠楁柟娉�锛�
3. 鐞嗚В Bernstein 瀹氱悊鍙� Cantor 灏�(du矛)瑙掔窔娉�銆�
浜�銆� Rn
涓殑鎷�?f霉)?br/>1. 鎺屾彙搴﹂噺姒傚康锛屽拰鐢辨寮曞嚭鐨勫収(n猫i)榛�(di菐n)锛岃仛榛�(di菐n)锛屽皫(d菐o)闆�锛岄枆鍖�锛岄枊(k膩i)闆嗚垏
闁夐泦绛夋蹇靛強鍏舵€ц唱(zh矛)锛�
2. 鐞嗚В 1 缍垏 2 缍互涓婃瓙寮忕┖闁撻枊(k膩i)闆嗙殑妲�(g貌u)閫犲畾鐞�锛屽苟鑳藉湪鍚庨潰鐨勬脯(c猫)
搴︾悊璜栦腑鎰忚瓨(sh铆)鍒板畠鍊戠殑鍗€(q奴)鍒ワ紱
3. 鎺屾彙瀹屽倷闆�锛岀枏鏈楅泦锛岀瀵嗛泦锛岀穵鑷撮泦绛夊熀鏈蹇�锛屽苟鑳藉皪(du矛)搴锋墭
锛圕antor锛変笁鍒嗛泦銆佸唬缇╁悍鎵橈紙Cantor锛夐泦鍋氱浉鎳�(y墨ng)鎺㈣◣銆�
涓�銆� 娓�(c猫)搴︾悊璜�
1. 鐞嗚В澶栨脯(c猫)搴�銆佹脯(c猫)搴︾殑姒傚康鍙婂叾鍗€(q奴)鍒�锛岃兘澶犻亱(y霉n)鐢� Caratheodory 姊�
浠舵帹灏�(d菐o) Lebesgue 鍙脯(c猫)闆嗗悇绋€ц唱(zh矛)锛�
2. 鎺屾彙涓嶅彲娓�(c猫)闆嗙殑妲�(g貌u)閫犳柟娉曡垏鐮村鍙垪鍙姞鎬х殑鍙嶄緥锛�
3. 鎺屾彙闁�(k膩i)闆�銆侀枆闆�銆丟?闆�銆丗?闆嗚垏鍙脯(c猫)闆嗙殑闂�(gu膩n)绯�锛岀啛绶撮亱(y霉n)鐢ㄧ瓑娓�(c猫)鍖�銆�
绛夋脯(c猫)鏍告蹇佃瓑鏄庨泦鍚堢殑鍙脯(c猫)鎬�锛�
4. 鐞嗚В浠ｆ暩(sh霉)銆�?浠ｆ暩(sh霉)銆丅orel 闆嗙殑姒傚康锛屾帉鎻� Borel 闆嗚垏 Lebesgue
鍙脯(c猫)闆嗙殑闂�(gu膩n)绯�銆�
鍥涖€� 鍙脯(c猫)鍑芥暩(sh霉)
1. 鐞嗚В鍙脯(c猫)鍑芥暩(sh霉)鑸囩啊(ji菐n)鍠嚱鏁�(sh霉)涔嬮枔鐨勯棞(gu膩n)绯�锛屽苟鑳界敤鍙脯(c猫)鍑芥暩(sh霉)鍩烘湰姒�
蹇点€佺啊(ji菐n)鍠嚱鏁�(sh霉)鍒楅€艰繎鍏╃ó鏂规硶璀夋槑鍚勭ó鎬ц唱(zh矛)锛�
2. 鎺屾彙鍙脯(c猫)鍑芥暩(sh霉)鍒楃殑閫愰粸(di菐n)鏀舵杺銆佽繎涓€鑷存敹鏂�銆佷緷娓�(c猫)搴︽敹鏂傜殑闂�(gu膩n)绯诲強
璀夋槑鏂规硶锛堝寘鎷憠鏋滄礇澶紙Egoroff锛夊畾鐞�锛岄粠鏂紙Riesz锛夊畾鐞嗭級锛�
鐞嗚В渚濇脯(c猫)搴︽敹鏂傜殑閲嶈鎬�锛�
3. 鎺屾彙閫ｇ簩(x霉)鍑芥暩(sh霉)鑸囧彲娓�(c猫)鍑芥暩(sh霉)鐨勯棞(gu膩n)绯伙紝鑳藉閬�(y霉n)鐢ㄩ閲戯紙Lusin锛夊畾鐞�
瑙ｆ焙鐩搁棞(gu膩n)鍟�(w猫n)椤�銆�
浜�銆� Lebesgue 绌嶅垎
1. 鎺屾彙 Lebesgue 绌嶅垎鐨勫畾缇╄垏鎬ц唱(zh矛)锛�
2. 鑳藉閬�(y霉n)鐢� Levi 寮曠悊銆丗adou 寮曠悊銆丩ebesgue 鎺у埗鏀舵杺瀹氱悊瑙ｆ焙
鍙脯(c猫)鍑芥暩(sh霉)鍒楃⿳鍒嗘敹鏂傚晱(w猫n)椤�锛岀悊瑙� Lebesgue 绌嶅垎鐨勭禃灏�(du矛)閫ｇ簩(x霉)鎬�锛�
3. 鐞嗚В Lebesgue 绌嶅垎鑸� Riemman 绌嶅垎鐨勯棞(gu膩n)绯�锛屽苟鑳芥摎(j霉)姝ら€�(j矛n)琛屽悇绋�
绌嶅垎閬�(y霉n)绠�锛�
4. 鐞嗚В閲嶇⿳鍒嗐€佺疮娆＄⿳鍒�銆丗ubini 瀹氱悊锛屽苟鑳介€�(j矛n)琛岀啊(ji菐n)鍠殑閬�(y霉n)绠�锛�
5. 鐞嗚В Vitali 瑕嗚搵銆佸柈瑾�(di脿o)鍑芥暩(sh霉)鐨� Lebesgue 瀹氱悊銆佹湁鐣岃畩宸嚱鏁�(sh霉)銆�
绲曞皪(du矛)閫ｇ簩(x霉)鍑芥暩(sh霉)銆丩ebesgue-Stieltjes 绌嶅垎銆�
鍙冮柋
銆婂(sh铆)璁婂嚱鏁�(sh霉)璜栥€嬶紙绗簩鐗堬級锛屽懆姘戝挤(qi谩ng)锛屽寳浜ぇ瀛�(xu茅)鍑虹増绀�锛�2008 骞�
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘�锛岃珛(q菒ng)鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄わ紝鍙︼細鏈枃鍍呬唬琛ㄤ綔鑰呭€�(g猫)浜鸿榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇(w煤)闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊(sh铆)锛屽皪(du矛)鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€�銆佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛(q菒ng)璁€鑰呭儏浣滃弮鑰�锛屽苟璜�(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹广€�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
