  In this article, a solution to the so-called Frisch-Parisi conjecture is
brought. This achievement is based on three ingredients developed in this
paper. First almost-doubling fully supported Radon measures on $\R^d$ with a
prescribed singularity spectrum are constructed. Second we define new
\textit{heterogeneous} Besov spaces $B^{\mu,p}_{q}$ and find a characterization
using wavelet coefficients. Finally, we fully describe the multifractal nature
of typical functions in the function spaces $B^{\mu,p}_{q}$. Combining these
three results, we find Baire function spaces in which typical functions have a
prescribed singularity spectrum and satisfy a multifractal formalism. This
yields an answer to the Frisch-Parisi conjecture.
