Abstract : In this paper, we prove that in the Baire category sense, measures supported by the unit cube of R(d) typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures mu. This spectrum appears to be linear with slope 1, starting from 0 at exponent 0, ending at dimension d at exponent d, and it indeed coincides with the Legendre transform of the L(q)-spectrum associated with typical measures mu.