Advances in Dynamical Systems and Control by Victor A. Sadovnichiy & Mikhail Z. Zgurovsky

Author:Victor A. Sadovnichiy & Mikhail Z. Zgurovsky
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(ii) is the identity operator on X,

(iii)(cocycle property) for all .

Definition 11.2

Let be a probability space. A random set K is a measurable subset of with respect to the product -algebra .

The -section of a random set K is defined by

In the case that a set has closed or compact -sections, it is a random set as soon as the mapping is measurable (from to ) for every , see [7]. Then, K will be said to be a closed or a compact, respectively, random set. It will be assumed that closed random sets satisfy for all or at least for -almost all .

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