Property A and asymptotic dimension

The purpose of this note is to characterize the asymptotic dimension asdim(X)
of metric spaces X in terms similar to Property A of Yu:

Theorem: If (X,d) is a metric space and n >= 0, then the following conditions are equivalent:
a. asdim(X,d) <= n,

b. For each R, epsilon > 0 there is S > 0 and finite non-empty subsets A_x of B(x,S) x N, x in X, such that 
             |A_x \Delta A_y|/|A_x \cap A_y| < epsilon if d(x,y) < R 
and the projection of A_x onto X contains at most n+1 elements for all  x in X,

c. For each R > 0 there is $S > 0$ and finite non-empty subsets A_x of B(x,S) x N, x in X, such that 
             |A_x \Delta A_y|/\A_x \cap A_y| < 1/(n+1) 
if d(x,y) < R and the projection of A_x onto X contains at most n+1 elements for all x in X.