Convergence of Deterministic IFS

First, note

S1 ⊆ S0 = (S0)0,

where the second subscript 0 indicates an e-thickening with e = 0.

To be sure S1 is thickened enough to cover all of S0, note we must cover the upper right corner of S0. To do this, thickening S1 by 1/2 suffices. That is, S0 ⊆ (S1)1/2, Consequently, h(S0, S1) = 1/2. Return to Hausdorff Distance Convergence Example.