Asymptotic $l_p$ spaces and bounded distortions
  The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class.   The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm. 
Vitali D. Milman, Nicole Tomczak-Jaegermann