ESTIMATE OF THE HAUSDORFF MEASURE OF THE SIERPINSKI TRIANGLE
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It is well-known that the Hausdorff dimension of the Sierpinski triangle Λ is s = log 3/ log 2. However, it is a long standing open problem to compute the s-dimensional Hausdorff measure of Λ denoted by [Formula: see text]. In the literature the best existing estimate is [Formula: see text] In this paper we improve significantly the lower bound. We also give an upper bound which is weaker than the one above but everybody can check it easily. Namely, we prove that [Formula: see text] holds.
2018 ◽
Vol 2020
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pp. 5797-5813
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2000 ◽
Vol 11
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pp. 1057-1078
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1991 ◽
Vol 11
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pp. 779-786
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2019 ◽
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pp. 3217-3235
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1992 ◽
Vol 12
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pp. 53-66
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