測度維數(shù)的局部化與函數(shù)圖象盒維數(shù)的若干研究.pdf

1、華中科技大學碩士學位論文測度維數(shù)的局部化與函數(shù)圖象盒維數(shù)的若干研究姓名：杜玉坤申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：朱三國20100522u??E??a?????AbstractThispaperconsidersthelocalizationofdimensionsofmeasurestheMinkowskidimensionofgraphsoffunctions.Fthestudyofthelocalizationofdimen

2、sionsofmeasuresthelocalizationofdimensionsofmeasuresatthepointxisfirstlygivenbywhichwecefinedimensionsofmeasuresitself.Atthesametimewhichwecanshowbydimensionsofsets.Thenwedefinemeasuresofx?thenthelocalizationofdimatthepo

3、intxisgivenwhichwecalldim?(x).Inpartthreeweshallconsidertherelationsbetweenthelocalizeddimensiondim?(x)theiginaldimensiondim?.FthestudyoftheMinkowskidimensionofgraphsoffunctionswefirstlygivethedefinitionsofgraphsoffuncti

4、onsLetf:I≡[01]→Rbeacontinuousfunction.WedenotebyΓ(fI)thegraphoffΓ(fI)=(xf(x)):x∈[01].thentheδ?offatthepointxisgivenatthesametimetheδ?offon[ab]isgiven.Fanyacontinuousfunctiontheupper(under)Minkowskidimensionofgraphsoffunc

5、tionsisdefined.AsweallknowifdimBΓ(fI)dimBΓ(gI)thendimBΓ(fgI)=dimBΓ(fI).Itisnaturaltoaskthefollowingquestions:1.whatcanwesayaboutdimBΓ(fgI)whendimBΓ(fI)=dimBΓ(gI)2.IsitpossiblethatdimBΓ(fgI)maxdimBΓ(fI)dimBΓ(gI)3.whatcanw

6、esayaboutdimBΓ(fgI)whendimBΓ(fI)dimBΓ(gI)Inpartfourweintroducethemainaimofthispaper.Letfgbecontinuousfunctionson[01].WearetoestablishsomebasicresultsontherelationshipsamongdimBΓ(fI)dimBΓ(gI)dimBΓ(fgI)dimBΓ(fgI)dimBΓ(fgI)