Find in Library

<p/> <p>Two new fractal measures <inline-formula><graphic file="1029-242X-2007-026249-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2007-026249-i2.gif"/></inline-formula> are constructed from Minkowski contents <inline-formula><graphic file="1029-242X-2007-026249-i3.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2007-026249-i4.gif"/></inline-formula>. The properties of these two new measures are studied. We show that the fractal dimensions Dim and <inline-formula><graphic file="1029-242X-2007-026249-i5.gif"/></inline-formula> can be derived from <inline-formula><graphic file="1029-242X-2007-026249-i6.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2007-026249-i7.gif"/></inline-formula>, respectively. Moreover, some inequalities about the dimension of product sets and product measures are obtained. </p>