  We investigate the relationship between algorithmic fractal dimensions and
the classical local fractal dimensions of outer measures in Euclidean spaces.
We introduce global and local optimality conditions for lower semicomputable
outer measures. We prove that globally optimal outer measures exist. Our main
theorem states that the classical local fractal dimensions of any locally
optimal outer measure coincide exactly with the algorithmic fractal dimensions.
Our proof uses an especially convenient locally optimal outer measure
$\boldsymbol{\kappa}$ defined in terms of Kolmogorov complexity. We discuss
implications for point-to-set principles.
