Two deficiencies in fractal phenomenology at high energies

It is shown that (i) the relation between scaling indices which characterize the presence of the intermittency and multifractality, and (ii) the equation which relates the scaling indices characterizing multifractality with the probabilities ascribed to the underlying dynamics, can be formulates - with appropriate extension - in such a consistent way which is compatible with the Satz' condition specifying the presence of the (thermal) phase transition. (author)