# A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

Analysis and Geometry in Metric Spaces (2013)

- Volume: 1, page 36-41
- ISSN: 2299-3274

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topGuy David, and Marie Snipes. "A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension." Analysis and Geometry in Metric Spaces 1 (2013): 36-41. <http://eudml.org/doc/267210>.

@article{GuyDavid2013,

abstract = {We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.},

author = {Guy David, Marie Snipes},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Assouad Embedding; doubling metric spaces; snowflake distance; Assouad embedding; Snowflake distance},

language = {eng},

pages = {36-41},

title = {A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension},

url = {http://eudml.org/doc/267210},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Guy David

AU - Marie Snipes

TI - A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

JO - Analysis and Geometry in Metric Spaces

PY - 2013

VL - 1

SP - 36

EP - 41

AB - We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.

LA - eng

KW - Assouad Embedding; doubling metric spaces; snowflake distance; Assouad embedding; Snowflake distance

UR - http://eudml.org/doc/267210

ER -

## References

top- P. Assouad, Plongements lipschitziens dans Rn, Bull. Soc. Math. France, 111(4), 429–448, 1983. Zbl0597.54015
- J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, 2001. Zbl0985.46008
- A. Naor and O. Neiman, Assouad’s theorem with dimension independent of the snowflaking, Revista Matemática Iberoamericana 28 (4), 1–21, 2012 [WoS] Zbl1260.46016

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