Abstract
We investigate the dimension of intersections of the Sierpiński-like carpets with lines. We show a sufficient condition that for a fixed rational slope the dimension of almost every intersection with respect to the natural measure is strictly greater than s–1 , and almost every intersection with respect to the Lebesgue measure is strictly less than s–1 , where s is the Hausdorff dimension of the carpet. Moreover, we give partial multifractal spectra for the Hausdorff and packing dimension of slices.
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