  By an appropriate definition, we divide the irregular set into level sets.
Then we characterize the multifractal spectrum of these new pieces by
calculating their entropies. We also compute the entropies of various
intersections of the level sets of regular and irregular set which is rarely
studied in the literature. Moreover, our conclusions also hold for the
topological pressure. Finally, we consider the continuous case and use our
results to give a description for the suspension flow.

Dynamical Systems