after much objection ..

I will write down carefully the David-Jones Theorem, directly from the Mattila text. So here it is:

For any positive integers m and n and ε > 0, there exists an integer N(ε) such that if Q is the unit cube in Rⁿ, m ≥ n, and if f : Q → R^m with Lip(f) = 1, then there are B₁, ..., B_N in Q, N ≥ N(&epsilon), such that

Hⁿ_∞[f(Q \ (B₁ u ... u B_N)] < ε

and each f|B_i is bi-Lipschitz with Lip((f|B_i)^-1) ≤ N(ε).

Sorry for the confusion and errata, guys. Let me think once or twice before I comment on this theorem again!