  We study the measure theoretic properties of typical C 0 maps of the
interval. We prove that any ergodic measure is pseudo-physical, and conversely,
any pseudo-physical measure is in the closure of the ergodic measures, as well
as in the closure of the atomic measures. We show that the set of
pseudo-physical measures is meager in the space of all invariant measures.
Finally, we study the entropy function. We construct pseudo-physical measures
with infinite entropy. We also prove that, for each m $\ge$ 1, there exists
infinitely many pseudo-physical measures with entropy log m, and deduce that
the entropy function is neither upper semi-continuous nor lower
semi-continuous.
