Finally, let B be any compact subset of the plane. Then because |
h(T (B), A) = h(T (B),T (A)) ≤ r⋅h(B,A) by Prop. 2 |
Iterating this argument, we obtain |
h(T k(B), A) ≤ rk⋅h(B, A) |
Because r < 1, we see |
limk→∞ h(T k(B), A) = 0. |
Return to Convergence of determinisitc IFS.