Generic properties of invariant measures for continuous piecewise monotonic transformations

We endow the set of all invariant measures of topologically transitive subsetsL withh_top (L)>0 of a continuous piecewise monotonic transformation on [0, 1] with the weak topology. We show that the set of periodic orbit measures is dense, that the sets of ergodic, of nonatomic, and of measures with supportL are denseG-sets, that the set of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a denseG-set.