| ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS |
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| 作者姓名： | Xu You Ren Fuyao |
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| 作者单位： | Institute of Mathematics，Fudan University，Shanghai 200433，China. |
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| 摘 要： | 1.IntroductionInthegeometryoffractals,Hausdorffmeasurealiddimensionplayaveryimportantrole.Olltheotherhand,therecelltilltroductionofpackingmeasureshasledtoagreaterunderstandillgofthegeometrictheoryoffractals,aspackingmeasuresbehaveillawnythatis'dual'toHausdoofmeasure8inmanyrespectsl2].Forexample,denotingHausdorffdimellsionandpackingdimensionbydimandDimrespectively,wehavedim(ExF)2dimE dimF,whileDim(ExF)5DimE DimF.Itiswell-kllowenthatifECRm,FCR",thenH(ExFW1T2)2b'H((E,W1)H(FW2)forsome…
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| 收稿时间： | 5/4/1993 12:00:00 AM |
| 修稿时间： | 1993/10/25 0:00:00 |
ON TAYLOR'S CONJECTURE ABOUT THE PACKING
MEASURES OF CARTESIAN PRODUCT SETS |
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| Xu You,Ren Fuyao.ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS[J].Chinese Annals of Mathematics,Series B,1996,17(1):121-126. |
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| Authors: | Xu You and Ren Fuyao |
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| Institution: | Institute of Mathematics, Fudan University,
Shanghai 200433, China. |
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| Abstract: | It is proved that if $E\subset {\bold R},F\subset {\bold R}^n$,
then $ \Cal P(E\times F,\varphi_1\varphi_2)\leq c\cdot \Cal P(E,\varphi_1)
\Cal P(E,\varphi_2)$,
where $\Cal P(\cdot ,\varphi )$ denotes the $\varphi$-packing measure,
$\varphi$ belongs to a class of Hausdorff functions, the positive constant
$c$ deponds only on $\varphi_1,\varphi_2$ and $n$. |
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| Keywords: | Packing measure Hausdorff measure Cartesian product set |
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