Generic properties of invariant measures for simple piecewise monotonic transformations (Q1098961)

For piecewise monotonic maps T on the interval [0,1], restricted to a topologically transitive subset L with positive topological entropy for \(T|_ L\) the author derives analogues to \textit{K. Sigmund}'s results in Invent. Math. 11, 99-109 (1970; Zbl 0193.355) for the space M of invariant measures of \(T|_ L:\) measures on periodic orbits are dense; ergodic (nonatomic) measures and measures \(\mu\) with \(\sup p \mu =L\) are dense \(G_{\delta}\)-sets in M; mixing measures are of first category and measures with zero entropy contain a dense \(G_{\delta}\)- set. The proof uses specification in a modified form.