Jan Mařík
Abstract
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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 $\alpha \in (0,2)$.
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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 $\alpha \in (0,2)$.
Key concepts: Hausdorff dimension, Mathematics, Plane (geometry), Dimension (graph theory), Point (geometry), Measure (data warehouse), Line (geometry), Geometry