ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS

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 $n$.