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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骞达紝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�鈥� 涓嬭級
绗� 1 闋� 鍏� 3 闋�
鏉窞闆诲瓙绉戞妧澶у(xu茅)
纰╁＋鐮旂┒鐢熷京(f霉)瑭﹀悓绛夊(xu茅)鍔涘姞瑭︾鐩€冭│澶х侗
瀛�(xu茅)闄細鐞嗗(xu茅)闄� 鍔犺│绉戠洰锛氬(sh铆)璁婂嚱鏁�(sh霉)
涓€銆侀泦鍚�
鑰冩煡鍏�(n猫i)瀹�
1锛庨泦鍚堝強鍏堕亱(y霉n)绠�銆�
2锛庨泦鍚堢殑鍕�(sh矛)銆�
3锛巒 缍┖闁撲腑鐨勯粸(di菐n)闆�銆�
鑰冩煡瑕佹眰
1锛庣啛绶存帉鎻￠泦鍚堢殑骞�銆佷氦銆佸樊锛堣(b菙)锛夐亱(y霉n)绠楀拰灏�(du矛)鍋跺師鐞�锛涙帉鎻′笂妤甸檺銆佷笅妤甸檺鐨勫畾缇╁強鍏剁瓑
鍍�(ji脿)琛ㄨ堪銆�
2锛庢帉鎻℃槧灏�銆佸皪(du矛)绛�銆侀泦鍚堝嫝(sh矛)绛夋蹇�锛屾渻(hu矛)鐢˙ernstein 瀹氱悊瑷庤珫闆嗗悎鐨勫嫝(sh矛)锛屾渻(hu矛)姣旇純闆嗗悎鍕�(sh矛)鐨�
澶у皬銆�
3锛庢帉鎻″彲鏁�(sh霉)闆嗘蹇佃垏鎬ц唱(zh矛)锛屾渻(hu矛)璀塠0,1]榛�(di菐n)闆嗕笉鍙暩(sh霉)锛屾帉鎻″叿鏈夐€ｇ簩(x霉)鍕�(sh矛)鐨勯泦锛屽啰闆嗗強鍏跺嫝(sh矛)銆�
4. 鎺屾彙鑱氶粸(di菐n)銆佸収(n猫i)榛�(di菐n)銆侀倞鐣岄粸(di菐n)銆佸皫(d菐o)闆�銆侀枆鍖�銆侀枊闆嗐€侀枆闆�銆佸畬鍌欓泦鐨勬蹇佃垏鐩搁棞(gu膩n)鎬ц唱(zh矛)銆�
5. 浜嗚В鐩寸窔涓婇枊銆侀枆闆嗗強瀹屽倷闆嗙殑妲�(g貌u)閫狅紝浜嗚ВCantor闆�銆�
浜屻€佹脯(c猫)搴﹁珫
鑰冩煡鍏�(n猫i)瀹�
1锛庡娓�(c猫)搴﹁垏鍙脯(c猫)闆�銆�
2锛嶭ebesgue 鍙脯(c猫)闆嗙殑绲�(ji茅)妲�(g貌u)銆�
鑰冩煡瑕佹眰
1锛庣悊瑙ｆ帉鎻�(L) 澶栨脯(c猫)搴︽蹇佃垏鎬ц唱(zh矛)锛岀煡閬撳彲鍒楅泦鐨勬脯(c猫)搴︾偤闆�锛屽崁(q奴)闁撶殑娓�(c猫)搴︾瓑浜庡叾楂旂⿳銆�
2锛庣悊瑙ｅ彲娓�(c猫)闆嗙殑 Caratheodory 姊濅欢锛屽彲娓�(c猫)闆嗙殑姒傚康鑸囨€ц唱(zh矛)銆�
3锛庝簡瑙� F? 鍨嬮泦銆丟? 鍨嬮泦浠ュ強娉㈤浄鐖鹃泦鐨勫畾缇�锛屾帉鎻″彲娓�(c猫)闆嗛銆佸彲娓�(c猫)闆嗚垏闁嬮泦銆侀枆闆嗙殑闂�(gu膩n)
绯诲強鍙伌(c猫)闆嗙祼(ji茅)妲�(g貌u)锛涗簡瑙ｇ暥(d膩ng)
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0m E ? 鏅�(sh铆)锛� E 涓繀鏈変笉鍙脯(c猫)闆嗗瓨鍦ㄣ€�
绗� 2 闋� 鍏� 3 闋�
涓�銆佸彲娓�(c猫)鍑芥暩(sh霉)
鑰冩煡鍏�(n猫i)瀹�
1锛庡彲娓�(c猫)鍑芥暩(sh霉)鐨勫畾缇╁強鍏舵€ц唱(zh矛)銆�
2锛庡彲娓�(c猫)鍑芥暩(sh霉)鐨勯€艰繎瀹氱悊銆�
鑰冩煡瑕佹眰
1锛庢帉鎻″彲娓�(c猫)鍑芥暩(sh霉)姒傚康鍙婄瓑鍍�(ji脿)琛ㄨ堪锛屾帉鎻″彲娓�(c猫)鍑芥暩(sh霉)灏�(du矛)浠ｆ暩(sh霉)銆佹サ闄愰亱(y霉n)绠楀皝闁夌瓑閲嶈鎬ц唱(zh矛)锛�
鎺屾彙鍛介鍦ㄩ粸(di菐n)闆嗗咕涔庤檿铏曟垚绔嬫蹇�锛涙帉鎻＄啊(ji菐n)鍠嚱鏁�(sh霉)鍙婂嚱鏁�(sh霉)鍦ㄩ粸(di菐n)闆嗛€ｇ簩(x霉)鐨勬蹇�銆�
2锛庢帉鎻″彲娓�(c猫)鍑芥暩(sh霉)鍒楀咕涔庤檿铏曟敹鏂傝垏涓€鑷存敹鏂傜殑闂�(gu膩n)绯�锛涙帉鎻goroff 瀹氱悊銆�
3锛庢帉鎻″彲娓�(c猫)鍑芥暩(sh霉)绲�(ji茅)妲�(g貌u)锛孡usin 瀹氱悊銆�
4锛庢帉鎻′緷娓�(c猫)搴︽敹鏂�銆佸咕涔庤檿铏曟敹鏂傚強锛堝熀鏈級涓€鑷存敹鏂備笁鑰呯殑闂�(gu膩n)绯�銆�
鍥�銆丩ebesgue 绌嶅垎
鑰冩煡鍏�(n猫i)瀹�
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3锛嶧ubini 瀹氱悊銆�
鑰冩煡瑕佹眰
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绌嶅垎鐨勬蹇�銆�
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4锛庣悊瑙� Lebesgue 绌嶅垎鑸囬粠鏇肩⿳鍒嗙殑鍗€(q奴)鍒ヨ垏鑱�(li谩n)绯�銆�
5锛庝簡瑙�(L)绌嶅垎鐨勫咕浣曟剰缇�锛屾渻(hu矛)闄宠堪骞舵噳(y墨ng)鐢ㄩ噸绌嶅垎鍖栫疮娆＄⿳鍒嗙殑 Fubini 瀹氱悊銆�
6锛庢帉鎻＄禃灏�(du矛)閫ｇ簩(x霉)鍑芥暩(sh霉)姒傚康锛�(L)涓嶅畾绌嶅垎鑸囩禃灏�(du矛)閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勯棞(gu膩n)绯�锛汵ewton-Leibniz鍏紡鎴愮珛
鐨勫厖瑕佹浠�銆�
鍙冭€冩浉鐩細锛堥伕鎿囧叾涓€锛�
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1.銆婂(sh铆)璁婂嚱鏁�(sh霉)璜栬垏娉涘嚱鍒嗘瀽銆�锛屾浌寤ｇ绶�锛岀涓夌増锛堜笂鍐�(c猫)锛�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2011锛�
2.銆婂(sh铆)璁婂嚱鏁�(sh霉)璜栬垏娉涘嚱鍒嗘瀽銆�锛屽閬撹绛夌法锛岀浜岀増锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2009锛�
3锛庛€婂(sh铆)璁婂嚱鏁�(sh霉)璜栥€�锛屾睙婢ゅ爡(ji膩n)绶紝绗簩鐗�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2001锛�
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�銆佹枃瀛楃殑鐪熷(sh铆)鎬с€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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鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
