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| ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS |
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Citation： |
Xu You,Ren Fuyao.ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS[J].Chinese Annals of Mathematics B,1996,17(1):121~126 |
| Page view： 855
Net amount： 634 |
Authors： |
Xu You; Ren Fuyao |
Foundation： |
Project supported by the Science Found of Chinese
Academy of Sciences |
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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 $n$. |
Keywords： |
Packing measure, Hausdorff measure, Cartesian product set |
Classification： |
28A12, 28A35 |
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