  We show that if $Z$ is "homogeneously multifractal" (in a sense we precisely
define), then $Z$ is the composition of a monofractal function $g$ with a time
subordinator $f$ (i.e. $f$ is the integral of a positive Borel measure
supported by $\zu$). When the initial function $Z$ is given, the monofractality
exponent of the associated function $g$ is uniquely determined. We study in
details a classical example of multifractal functions $Z$, for which we exhibit
the associated functions $g$ and $f$. This provides new insights into the
understanding of multifractal behaviors of functions.
