Geodesic
The Hausdorff dimension of some special plane sets
Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 359-366

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MR Zbl
A compact set $T\subset \bold R^2$ is constructed such that each horizontal or vertical line intersects $T$ in at most one point while the $\alpha$-dimensional measure of $T$ is infinite for every $\alpha \in (0,2)$.
A compact set $T\subset \bold R^2$ is constructed such that each horizontal or vertical line intersects $T$ in at most one point while the $\alpha$-dimensional measure of $T$ is infinite for every $\alpha \in (0,2)$.
DOI : 10.21136/MB.1994.126119
Classification : 28A05, 28A78
Keywords: Hausdorff dimension; compact plane set; Hausdorff measure 
Mařík, Jan. The Hausdorff dimension of some special plane sets. Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 359-366. doi: 10.21136/MB.1994.126119
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[1] S. Saks: Theory of the integral. Dover Publications, 1964. | MR

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