Geodesic
The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems
Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 217-226

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We obtain conditions that allow one to evaluate the relative frequency of occurrence of the reachable set of a control system in a given set. If the relative frequency of occurrence in this set is $1$, then the set is said to be statistically invariant. It is assumed that the images of the right-hand side of the differential inclusion corresponding to the given control system are convex, closed, but not necessarily compact. We also study the basic properties of the space $\mathrm{clcv}(\mathbb R^n)$ of nonempty closed convex subsets of $\mathbb R^n$ with the Hausdorff–Bebutov metric. 
@article{TRSPY_2012_278_a19,
     author = {L. I. Rodina},
     title = {The space $\mathrm{clcv}(\mathbb R^n)$ with the {Hausdorff--Bebutov} metric and statistically invariant sets of control systems},
     journal = {Informatics and Automation},
     pages = {217--226},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/}
}
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L. I. Rodina. The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems. Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 217-226. http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/