Some ergodic theorems for piecewise monotonic transformations (Q1922990)

The paper contains various ergodic theorems for the Frobenius-Perron operator and for the composition of piecewise strictly expanding interval maps. They all are immediate corollaries to classical results cited from \textit{N. Dunford} and \textit{J. T. Schwartz}: ``Linear operators, Part I'' (1958; Zbl 0084.10402) combined with the variation estimates by \textit{A. Lasota} and \textit{J. A. Yorke} [Trans. Am. Math. Soc. 186, 481-488 (1974; Zbl 0298.28015)]. None of them is new. The same is true for the class of piecewise convex maps also considered in this paper, which, in fact, form a subclass of the class of operators studied by Lasota and Yorke.