Undecidably semilocalizable metric measure spaces.

We characterize measure spaces such that the canonical map L ∞ → L 1 ∗ is surjective. In case of d -dimensional Hausdorff measure on a complete separable metric space X , we give two equivalent conditions. We give examples of X and d so that whether these conditions are met is undecidable in ZFC, including one with d equals the Hausdorff dimension of X. [ABSTRACT FROM AUTHOR]