A few problems connected with invariant measures of Markov maps -- verification of some claims and opinions that circulate in the literature (Q1987062)

\textit{A. Lasota} and \textit{J. A. Yorke} [Trans. Am. Math. Soc. 186, 481--488 (1974; Zbl 0298.28015)] gave conditions on piecewise \(C^2\) maps of the interval that guarantee the existence of an absolutely continuous invariant measure. Various attempts to relax the conditions, and in particular to extend to countably many branches, have been made. This history is recalled here, and in particular some subtle errors in the literature are explained. The authors systematically develop the known results and illustrate some of the problems and possible confusions that have arisen via examples.