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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�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骞达紝2013骞�锛涘潎鎻愪緵鏀惰不涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛炴搳鈥�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛炴搳鈥�鑰冨崥瑭﹀嵎搴�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│绉戠洰锛氬璁婂嚱鏁�(sh霉)
瑭﹀嵎婊垮垎鍙婅€冭│鏅傞枔锛氳│鍗锋豢鍒嗙偤 100 鍒嗭紝鑰冭│鏅傞枔鐐� 180 鍒嗛悩銆�
鑰冭│鍏�(n猫i)瀹�
涓€銆� 闆嗗悎璜栧熀绀�(ch菙)
1. 闆嗗悎鍙婂叾閬嬬畻锛�
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�銆�
浜�銆� Rn
涓殑鎷�?f霉)?br/>1. 闁嬮泦鑸囬枆闆�锛屽収(n猫i)榛�锛岃仛榛烇紝灏�(d菐o)闆�锛岄枆鍖� 锛�
2. 闁嬮泦鐨勬(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�
涓夈€� 娓害鐞嗚珫
1. 澶栨脯搴︾殑姒傚康鍜屽熀鏈€ц唱(zh矛)锛�
2. Lebesgue 鍙脯闆嗙殑姒傚康鑸� Caratheodory 姊濅欢锛�
3. Lebesgue 鍙脯闆嗗叏楂�?鐨勫悇绋暣楂旀€ц唱(zh矛)锛堝鍙垪鍙姞鎬х瓑锛�锛�
4. 涓嶅彲娓泦鐨勬(g貌u)閫狅紱
5. Lebesgue 鍙脯闆嗙殑绛夊児姒傚康锛�
6. 浠ｆ暩(sh霉)锛�?浠ｆ暩(sh霉)锛孊orel 闆�銆�
鍥涖€� 鍙脯鍑芥暩(sh霉)
1. 鍙脯鍑芥暩(sh霉)鍙婂叾鎬ц唱(zh矛)锛�
2. 娓嚱鏁�(sh霉)鍒楃殑閫愰粸鏀舵杺銆佽繎涓€鑷存敹鏂�銆佷緷娓害鏀舵杺锛�
3. 鐢ㄩ€ｇ簩(x霉)鍑芥暩(sh霉)閫艰繎鍙脯鍑芥暩(sh霉)锛岄閲戯紙Lusin锛夊畾鐞�銆�
浜�銆� Lebesgue 绌嶅垎
1. Lebesgue 绌嶅垎鐨勫畾缇╄垏鎬ц唱(zh矛)锛�
2. 鍙脯鍑芥暩(sh霉)鍒楃⿳鍒嗘敹鏂傚畾鐞�锛孡ebesgue 绌嶅垎鐨勭禃灏嶉€ｇ簩(x霉)鎬�锛�
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)锛岀禃灏嶉€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閬嬬畻锛堝寘鎷泦鍚堝垪鐨勪笂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▓绠楁柟娉�锛�
3. 鐞嗚В Bernstein 瀹氱悊鍙� Cantor 灏嶈绶氭硶銆�
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�锛岃仛榛烇紝灏�(d菐o)闆�锛岄枆鍖�锛岄枊闆嗚垏
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┖闁撻枊闆嗙殑妲�(g貌u)閫犲畾鐞�锛屽苟鑳藉湪鍚庨潰鐨勬脯
搴︾悊璜栦腑鎰忚瓨鍒板畠鍊戠殑鍗€(q奴)鍒�锛�
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� 娓害鐞嗚珫
1. 鐞嗚В澶栨脯搴�銆佹脯搴︾殑姒傚康鍙婂叾鍗€(q奴)鍒�锛岃兘澶犻亱鐢� Caratheodory 姊�
浠舵帹灏�(d菐o) Lebesgue 鍙脯闆嗗悇绋€ц唱(zh矛)锛�
2. 鎺屾彙涓嶅彲娓泦鐨勬(g貌u)閫犳柟娉曡垏鐮村鍙垪鍙姞鎬х殑鍙嶄緥锛�
3. 鎺屾彙闁嬮泦銆侀枆闆�銆丟?闆�銆丗?闆嗚垏鍙脯闆嗙殑闂�(gu膩n)绯�锛岀啛绶撮亱鐢ㄧ瓑娓寘銆�
绛夋脯鏍告蹇佃瓑鏄庨泦鍚堢殑鍙脯鎬�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
鍙脯闆嗙殑闂�(gu膩n)绯�銆�
鍥�銆� 鍙脯鍑芥暩(sh霉)
1. 鐞嗚В鍙脯鍑芥暩(sh霉)鑸囩啊鍠嚱鏁�(sh霉)涔嬮枔鐨勯棞(gu膩n)绯�锛屽苟鑳界敤鍙脯鍑芥暩(sh霉)鍩烘湰姒�
蹇�銆佺啊鍠嚱鏁�(sh霉)鍒楅€艰繎鍏╃ó鏂规硶璀夋槑鍚勭ó鎬ц唱(zh矛)锛�
2. 鎺屾彙鍙脯鍑芥暩(sh霉)鍒楃殑閫愰粸鏀舵杺銆佽繎涓€鑷存敹鏂�銆佷緷娓害鏀舵杺鐨勯棞(gu膩n)绯诲強
璀夋槑鏂规硶锛堝寘鎷憠鏋滄礇澶紙Egoroff锛夊畾鐞嗭紝榛庢柉锛圧iesz锛夊畾鐞嗭級锛�
鐞嗚В渚濇脯搴︽敹鏂傜殑閲嶈鎬�锛�
3. 鎺屾彙閫ｇ簩(x霉)鍑芥暩(sh霉)鑸囧彲娓嚱鏁�(sh霉)鐨勯棞(gu膩n)绯�锛岃兘澶犻亱鐢ㄩ閲戯紙Lusin锛夊畾鐞�
瑙ｆ焙鐩搁棞(gu膩n)鍟忛銆�
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. 鑳藉閬嬬敤 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
鍙脯鍑芥暩(sh霉)鍒楃⿳鍒嗘敹鏂傚晱椤�锛岀悊瑙� Lebesgue 绌嶅垎鐨勭禃灏嶉€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�
绌嶅垎閬嬬畻锛�
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)琛岀啊鍠殑閬嬬畻锛�
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�
绲曞皪閫ｇ簩(x霉)鍑芥暩(sh霉)銆丩ebesgue-Stieltjes 绌嶅垎銆�
鍙冮柋
銆婂璁婂嚱鏁�(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€嬩汉瑙€榛�锛岃垏鏈恫(w菐ng)绔欑劇闂�(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)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€с€佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂�(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� 
