Generic properties of invariant measures for continuous piecewise monotonic transformations (Q1118850)

We endow the set of all invariant measures of topologically transitive subsets L with \(h_{top}(L)>0\) 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 support L are dense \(G_{\delta}\)-sets, that the set of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a dense \(G_{\delta}\)-set.