  The multifractal formalism for measures hold whenever the existence of
corresponding Gibbs-like measures supported on the singularities sets holds. In
the present work we tried to relax such a hypothesis and introduce a more
general framework of mixed (and thus single) multifractal analysis where the
measures constructed on the singularities sets are not Gibbs but controlled by
an extra-function allowing the multifractal formalism to hold. We fall on the
classical case by a particular choice of such a function.
