Kurzbeschreibung: The (upper) L^q spectrum of a measure, which encodes a lot of its multifractal behaviour, can be characterized as the critical exponent for which a specific series converges. In my last talk, I generalized this to the critical exponent of other series. In this talk, it is generalized further, replacing series convergence with integrability. What results are retained and what this generalization can be applied to is discussed.