The Mathematics of Paul Erdős I pp 533-540 | Cite as

# On Lipschitz Mappings Onto a Square

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## Abstract

The following problem was posed by Laczkovich [5]: Let \(E \subseteq \mathbb{R}{\mathbb{R}}^{d}\) (*d* ≥ 2) be a set with positive Lebesgue measure *λ* ^{ d }(*E*) > 0. Does there exist a Lipschitz mapping \(f : {\mathbb{R}}^{d} \rightarrow Q = {[0,1]}^{d}\), such that *f*(*E*) = *Q*? Preiss [6] answered this question affirmatively for *d* = 2:

## Notes

### Acknowledgements

I would like to thank David Preiss for explaining me his proof, useful discussions and for his hospitality during my visit.

## References

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