The following problem was posed by Laczkovich [5]: Let E⊆RRd (d ≥ 2) be a set with positive Lebesgue measure λ d (E) > 0. Does there exist a Lipschitz mapping f:Rd → Q=[0,1]d|, such that f(E) = Q? Preiss [6] answered this question affirmatively for d= 2:
CITATION STYLE
Matoušek, J. (2013). On lipschitz mappings onto a square. In The Mathematics of Paul Erdos I, Second Edition (pp. 533–540). Springer New York. https://doi.org/10.1007/978-1-4614-7258-2_33
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