The Centered Hausdorff Measure of the Sierpiński Gasket

Abstract

We show that the centered Hausdorff measure, [Formula: see text] with [Formula: see text] of the Sierpiński gasket [Formula: see text], is [Formula: see text]-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 [Formula: see text] is [Formula: see text]-computable (algorithmic-computable) in the sense that there is an algorithm that converges to [Formula: see text], with explicit error bounds. Using this algorithm we show that [Formula: see text]1.0049.