Invariant measures of set-valued maps
The author remarks that standard definition of an invariant measure requires that the function be univalued. However, recent applications [cf. \textit{Z. Artstein}, J. Differential Equations 152, No. 2, 289-307 (1999; Zbl 0923.34013)] have raised the need for an analogous notion of invariant measures for multifunctions. The author in this very interesting paper displayed five natural suggestions for the notion and examined when they are equivalent. It is proved that four of his definitions are equivalent when the underlying space is is a separable and complete metric space, and the fifth one is equivalent to them if, in addition, the space is locally compact and the set-valued map has a closed graph.
scientific article; zbMATH DE number 1563087