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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�锛岄儴鍒嗗鏍℃洿鏂拌嚦2012骞�锛�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
闀锋槬鐞嗗伐澶у鏁�(sh霉)瀛哥爺绌剁敓鍏ュ鍔犺│
銆婂璁婂嚱鏁�(sh霉)鑸囨硾鍑藉垎鏋愩€嬭€冭│澶х侗
涓€銆佺附楂旇姹�
鑰冪敓鎳�(y墨ng)鎸夋湰澶х侗鐨勮姹�锛屾帉鎻� Lebesgue 鐨勬脯搴﹁珫锛屽璁婇噺鐨勫彲娓嚱鏁�(sh霉)鐞嗚珫锛孡ebesgue
绌嶅垎鐞嗚珫鑸囧井鍒嗙悊璜�锛屾帉鎻″害閲忕┖闁撳拰璩﹁寖绶氭€х┖闁撶殑姒傚康鍜屼緥瀛�锛屾湁鐣岀窔鎬х畻瀛愬拰閫ｇ簩(x霉)绶�
鎬ф硾鍑界殑姒傚康鍜屼緥瀛�锛屾帉鎻� Hilbert 绌洪枔鐨勫熀鏈€ц唱(zh矛)銆傝純濂界殑鎺屾彙娓害璜栬垏鎶借薄绌嶅垎鐞嗚珫锛�
骞朵笖鍦ㄤ竴瀹氱▼搴︿笂鎺屾彙闆嗗悎鐨勫垎鏋愭柟娉曘€�
浜�銆佹暀鏉�
銆婂璁婂嚱鏁�(sh霉)鑸囨硾鍑藉垎鏋愬熀绀�(ch菙)(绗簩鐗堬級銆�锛岀▼鍏惰绛夛紝楂樼瓑鏁欒偛鍑虹増绀�,2003.
涓�銆佽€冭│鍏�(n猫i)瀹�
锛堜竴锛� 闆嗗悎
1. 鎺屾彙闆嗗悎鐨勬蹇�锛岄泦鍚堢殑鍖呭惈鍜岀浉绛夌殑闂�(gu膩n)绯诲拰鍒ゅ畾鏂规硶锛�
2. 鐔熺反鎺屾彙闆嗗悎鐨勫拰銆佷氦銆佸樊銆佷綑鐨勯亱绠楋紝鎺屾彙涓婇檺闆�銆佷笅闄愰泦鍜屾敹鏂傞泦鐨勫畾缇�
3. 鏈冩眰闆嗗悎鐨勫拰銆佷氦銆佸樊銆佷綑锛屾渻姹傞泦鍚堟棌鐨勪笂闄愰泦銆佷笅闄愰泦锛屾渻鍒ゅ畾闆嗗悎鍒楁槸鍚︽敹
鏂傦紱
4. 鐞嗚В闆嗗悎鍩烘暩(sh霉)鐨勬蹇�锛屽皪绛夌殑姒傚康锛屾帉鎻� Bernstein 瀹氱悊锛屾渻鐢� Bernstein 瀹氱悊鍒�
瀹氶泦鍚堝皪绛夛紱
5. 鎺屾彙鍙暩(sh霉)闆嗗悎鑸囧叿鏈夐€ｇ簩(x霉)鍩烘暩(sh霉)鐨勪笉鍙暩(sh霉)闆嗗悎鐨勬蹇�銆佷緥瀛愬拰閬嬬畻鎬ц唱(zh矛)锛岃兘澶犲埄鐢ㄥ凡
鐭ョ殑渚嬪瓙鍜岄亱绠楁€ц唱(zh矛)鍘荤⒑瀹氶泦鍚堢偤鍝鐒￠檺闆嗗悎锛�
6. 鐭ラ亾涓嶅瓨鍦ㄥ叿鏈夋渶澶у熀鏁�(sh霉)鐨勯泦鍚�銆�
锛堜簩锛夐粸闆�
1. 鐞嗚В璺濋洟鍜岃窛闆㈢┖闁撶殑姒傚康锛屾噦寰� Euclid 绌洪枔鏄窛闆㈢┖闁�锛�
2. 鎺屾彙閯板煙鐨勬蹇佃垏鎬ц唱(zh矛)锛屾帉鎻￠粸鍒楁敹鏂�銆侀粸闆嗚窛闆�銆佹湁鐣岄泦鍜屽崁(q奴)闁撶殑姒傚康锛�
3锛庢繁鍏ョ悊瑙ｅ収(n猫i)榛�銆佸榛�銆佺晫榛�銆佽仛榛�銆佸绔嬮粸鐨勫畾缇�锛岀悊瑙ｅ苟鎺屾彙闆嗗悎鐨勯枊鏍搞€佸皫(d菐o)闆�銆�
閭婄晫銆侀枆鍖呯殑姒傚康鍙婄浉闂�(gu膩n)鐨勬€ц唱(zh矛)锛�
4. 鐔熺反鎺屾彙闁嬮泦銆侀枆闆嗙殑姒傚康鍜岀浉闂�(gu膩n)鎬ц唱(zh矛)锛屾帉鎻＄穵闆嗙殑姒傚康锛屽畬鍌欓泦鐨勬蹇�锛屾帉鎻℃湁
闄愯钃嬪畾鐞�锛�
5. 鐞嗚В鐩寸窔涓婇枊闆�銆侀枆闆嗙殑妲�(g貌u)閫犲畾鐞�锛屾帉鎻� Cantor 闆嗙殑鎬ц唱(zh矛)銆�
锛堜笁锛夋脯搴﹁珫
1.娣卞叆鐞嗚В骞剁啛绶存帉鎻″娓害锛孡-鍙脯闆嗙殑瀹氱京鍜屽熀鏈€ц唱(zh矛)锛屽苟鎺屾彙鍏稿瀷鐨勪緥瀛�
2.鐞嗚В? 浠ｆ暩(sh霉)鐨勫畾缇╋紝鎺屾彙 Borel 闆�銆丟? 鍨嬮泦銆丗? 鍨嬮泦鐨勫畾缇�锛屾槑纰哄彲娓泦鍜� Borel
闆�銆� G? 鍨嬮泦銆� F? 鍨嬮泦涔嬮枔鐨勯棞(gu膩n)绯�锛屾帉鎻� L-鍙脯闆嗛锛�
锛堝洓锛夊彲娓嚱鏁�(sh霉)
1. 鐞嗚В骞舵帉鎻″彲娓嚱鏁�(sh霉)鐨勫畾缇╄垏绛夊児姊濅欢锛屾帉鎻＄啊鍠嚱鏁�(sh霉)鐨勬蹇�锛屽咕涔庤檿铏曟敹鏂傜殑姒�
蹇�锛岀悊瑙ｇ啊鍠嚱鏁�(sh霉)鑸囧彲娓嚱鏁�(sh霉)鐨勯棞(gu膩n)绯�锛�
2. 鐞嗚В Egorov 瀹氱悊锛孡usin 瀹氱悊锛�
3. 鐞嗚В骞舵帉鎻′緷娓害鏀舵杺鐨勫畾缇�锛岀悊瑙� Riesz 瀹氱悊锛孡ebesgue 瀹氱悊锛屾渻鍒╃敤閫欏叐鍊嬪畾
鐞嗗幓瑙ｆ焙瀵﹂殯鍟忛銆�
锛堜簲锛夌⿳鍒嗚珫
1. 鐞嗚В骞剁啛绶存帉鎻� Lebesgue 绌嶅垎鐨勫畾缇╁拰绛夊児姊濅欢锛屾槑纰� L-鍙⿳鍑芥暩(sh霉)鐨勭ó椤�锛�
2. 鐔熺反鎺屾彙 L-绌嶅垎鐨勬€ц唱(zh矛)锛氱壒鍒ユ槸 Lebesgue 鎺у埗鏀舵杺瀹氱悊锛孡evi 瀹氱悊锛岄€愰爡绌嶅垎瀹�
鐞�锛岀⿳鍒嗙殑鍙暩(sh霉)鍙姞鎬э紝F(xi脿n)atou 寮曠悊锛岃兘澶犵啛绶村湴鍒╃敤閫欎簺鎬ц唱(zh矛)瑙ｆ焙瀵﹂殯鍟忛锛�
3. 鐭ラ亾 L-绌嶅垎鑸� R-绌嶅垎鐨勯棞(gu膩n)绯�锛涚悊瑙� Lebesgue 绌嶅垎鐨勫咕浣曟剰缇╁強 Fubini 瀹氱悊銆�
锛堝叚锛夊井鍒嗚垏涓嶅畾绌嶅垎
1. 鎺屾彙鍠(di脿o)鍑芥暩(sh霉)銆佹湁鐣岃畩宸嚱鏁�(sh霉)鐨勫彲寰€у拰鍏跺井鍒嗙殑 L-鍙⿳鎬�,鎺屾彙涓嶅畾绌嶅垎鐨勬蹇碉紝
绲曞皪閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬蹇�锛屼互鍙� L-鍙⿳鍑芥暩(sh霉)鐨� Newton-Leibniz 鍏紡锛�
2. 鐞嗚В鍒嗘绌嶅垎娉�锛�
3. 浜嗚В Steiltjes 绌嶅垎銆�
锛堜竷锛夊害閲忕┖闁撳拰璩﹁寖绶氭€х┖闁�
1. 鐞嗚В骞剁啛绶存帉鎻″害閲忕┖闁撲腑鐨勭浉闂�(gu膩n)姒傚康鍜屾€ц唱(zh矛)锛岀壒鍒ユ槸鍙垎绌洪枔锛屽畬鍌欏害閲忕┖闁擄紝
搴﹂噺绌洪枔鐨勫畬鍌欏寲鍏悊锛屽绺奖灏勫師鐞嗗強鎳�(y墨ng)鐢�锛�
鐞嗚В骞舵帉鎻¤肠鑼冪窔鎬х┖闁撶殑瀹氱京锛屼緥瀛�锛涙帉鎻� Banach 绌洪枔鐨勫畾缇╋紝渚嬪瓙鍜屾€ц唱(zh矛)銆�
锛堝叓锛夋湁鐣岀窔鎬х畻瀛愬拰閫ｇ簩(x霉)绶氭€ф硾鍑�
1. 鐞嗚В骞舵帉鎻℃湁鐣岀窔鎬х畻瀛�锛岀劇鐣岀窔鎬х畻瀛�锛岄€ｇ簩(x霉)绶氭€ф硾鍑界殑瀹氱京鍜屼緥瀛愶紱
2.鐞嗚В骞舵帉鎻＄畻瀛愯寖鏁�(sh霉)鐨勫畾缇�锛屾渻姹傜啊鍠殑绠楀瓙鑼冩暩(sh霉)锛�
3.鐞嗚В骞舵帉鎻℃湁鐣岀窔鎬х畻瀛愮┖闁撳強鍏跺叡杌涚┖闁撶殑瀹氱京锛屼緥瀛愶紝鍙婄啊鍠殑鎬ц唱(zh矛)锛屾渻姹傜啊鍠�
鐨勭窔鎬х畻瀛愮┖闁撶殑鍏辫粵绌洪枔锛�
4.浜嗚В寤ｇ京鍑芥暩(sh霉)鐨勫畾缇╁拰渚嬪瓙銆�
锛堜節锛� Hilbert 绌洪枔
1. 鎺屾彙鍏�(n猫i)绌嶇┖闁撶殑瀹氱京锛孒ilbert 绌洪枔鐨勫畾缇╁拰渚嬪瓙锛屾槑纰哄収(n猫i)绌嶇┖闁撲腑鑼冩暩(sh霉)銆佽窛闆㈠強
姝ｄ氦鐨勫畾缇╋紱
2. 鐞嗚В骞舵帉鎻� Hilbert 绌洪枔涓殑鎶曞奖瀹氱悊锛�
3. 鎺屾彙瑕�(gu墨)鑼冩浜ょ郴锛孎(xi脿n)ourier 绯绘暩(sh霉)鐨勫畾缇╋紝鐞嗚В骞舵帉鎻″畬鍏ㄨ(gu墨)鑼冩浜ょ郴锛孎(xi脿n)ourier 灞曢枊
寮忕殑姒傚康锛屾帉鎻″畬鍏ㄨ(gu墨)鑼冩浜ょ郴鐨勭瓑鍍规浠�锛屽垽瀹氬畾鐞嗭紝浠ュ強 Hilbert 绌洪枔涓畬鍏ㄨ(gu墨)鑼冩浜�
绯荤殑瀛樺湪鎬�锛�
4. 鎺屾彙 Riesz 琛ㄧず瀹氱悊锛屽叡杌涚畻瀛愮殑姒傚康鍙婃€ц唱(zh矛)锛�
5. 浜嗚В鑷即绠楀瓙锛岄厜绠楀瓙鍜屾甯哥畻瀛愮殑瀹氱京鍜岀啊鍠€ц唱(zh矛)銆�
鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘紝璜嬭伅(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛烇紝鑸囨湰缍�(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�銆佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰冿紝骞惰珛鑷鏍稿鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
