For a Radon measure μ and q,t ∈ R,let H_μ~q,t and P_μ~q,t denote the multifractal Hausdorff measure and the multifractal packing measure introduced in [L.Olsen, A Multifractal Formalism, Advances in Mathematics 116 (1996),82-196]. Let t蔙. We study the descriptive set theoretic complexity of the maps: K(R~d) Xμ(R~d) X R -> R:(K, μ,q) -> K_μ~q,t (K), K(R~d) Xμ(R~d) X R-> R:(K, μ,q) -> P_μ~q,t(K), and related multifractal measure and multifractal dimension maps: here K(R~d) denotes the family of non-empty compact subsets of R~d equipped with the Hausdorff metric ,and M(R~d) denotes the family of Radon measures on R~d eqipped with the weak topology.
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