Abstract
Abstract The multifractal formalism for measures holds 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 joint 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. An answer to a question raised in [2] on which gauge function φ shall we get a finite, infinite or zero value of H μ , φ q , t ( K ) for the singularities set K is provided.
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