關(guān)于ORLICZ-PETTIS定理的研究.pdf

1、哈爾濱工業(yè)大學(xué)碩士學(xué)位論文關(guān)于LICZPETTIS定理的研究姓名：孫李紅申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李容錄20050601哈爾濱工業(yè)大學(xué)理學(xué)碩L學(xué)位論文AbstractThe0rliczPettisTheoremisoneofthemostinterestingandusefulresultsinfunctionalanalysisSinceafeWdecades，themathematicianspassthrought

2、heunremittingendeavor，theynotonlywillstudythescopefromtobestowonthenormspacetopromotetothelocallyconvexspace，evenisthemetricspaceMoreoverthesubseriesconvergenceexpandsunceasinglyastheinvariablescopeUntilfindingthestronge

3、stOrlicz—PettistopologyThestrongestOrlicz—PettistopologyandthelargestmappingsfamilyFwhichyieldsthistopologyinabstractdualitypairwerefirstobtainedbyprofessorLiRongluin2000Inthispaperweintroducethattheuniformlyconvergentto

4、pologyinbothconditionallyo(F，E)一sequentiallyconvergentsubsetsofFand盯(F，￡)countablycompactsubsetsofFandtheweaktopologyhavethesamesubseriesconvergentseriesforlocallyconvexspace，F(xiàn)inally，1gaveanespecialexampleofthetheorem，an

5、dit’SprovedwithAntosik—Mikusinskibasicmetrictheoremietheuniformlytopologybothconditionala(ca(X，x)，∑)一sequentlycompactsubsetsofca(2，爿)anda(ca(2，x)，∑)countablycompactsubsetsofca(E，x)andcr(Z，ca(Z，上))一topologyhavethesamesubs

6、eriesconvergentseriesThussomefamoustheoremsuchastheVitaliHahn—SaksandNikondymconvergenceinclassicalmeasuretheoryareimprovedKeywordsabstractdualitypair；Orlicz—PettistopologY；uniformlyconvergenttopology；subseriesconvergenc