THE CENTERED HAUSDORFF MEASURE OF THE SIERPINSKI GASKET

We show that the centered Hausdorff measure, C-s(S), with s = log 3/log 2, of the Sierpinski gasket S, is C-computable (continuous-computable), in the sense that its value is the solution of the minimization problem of a continuous function on a compact domain. We also show that C-s(S) is A-computable (algorithmic-computable) in the sense that there is an algorithm that converges to C-s(S), with explicit error bounds. Using this algorithm we show that C-s(S) similar to 1.0049.