某些分形集的維數(shù)、測度及測度的密度.pdf

1、湖南師范大學碩士學位論文某些分形集的維數(shù)、測度及測度的密度姓名：尹杰申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：董新漢20080301ABSTRACTInthefirstpart，weexplorethedensityofthemiddlefifthCantormeaesureLetFo(z)=z／5，R(z)=x／52／5，易(z)=z／s4／sLetEbetheattractorofIFSF0，F(xiàn)1，F(xiàn)2Itiseasytoseeth

2、atEisamiddlefifthCantorsetLet衄beamiddlefifthCantormeasureLet8=log3／log5，weshaugiveadefiniteformulaoflowersdensity』r(pF，z)foreverypointz∈EWealsogiveaconclusionthat』r(pE，z)=4一。for#Ealmostallz∈EOnbasisoftheaboveresults，wepr

3、ovethatthesdimensionalpackingmeasureofEis妒Inthesecondpartofthisthesis，weintroducetheconceptof／2dimensionsWealsogivetwoexamplestoillustratethemLetpbeapositiveboundedregularBorelmeasureonRnwithboundedsupportForr0，1P00，theu

4、pper／2dimensionof蘆isdefinedby—dirnp臚li霉msu觜，r—0U，一衛(wèi)Jl【)g7’whereQ(r))denotethefamilyofrmeshcubesInthelastpart，wepatchupagapintheproofofanexampleintext”TheexampleshowsthatthedimensionofgraphofWeierstrassfunctionis8when入isl