The paper by Katz, Karin Usadi; Katz, M.: Bi-Lipschitz approximation by finite-dimensional imbeddings may be found at arXiv:0902.3126

Here it is shown that the Kuratowski imbedding of a Riemannian
manifold in L^{∞}, exploited in Gromov's proof of the
systolic inequality for essential manifolds, admits an approximation
by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding
for every C>0. The key tool is the first variation formula thought of
as a real statement in first-order logic, in the context of
non-standard analysis.

In a related development:

After years of institutionalized denial, research mathematician reveals: .999... can be less than 1, almost everywhere. Read all about it here

Robert Ely's paper examines nonstandard student conceptions

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