The authors claim that for continuous random dynamical systems with countable amenable group actions, normalized information functions converge to fiber entropy, and in the ergodic case to the fiber entropy value.
Actions of amenable groups
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The Shannon-McMillan-Breiman theorem of random dynamical systems for amenable group actions
The authors claim that for continuous random dynamical systems with countable amenable group actions, normalized information functions converge to fiber entropy, and in the ergodic case to the fiber entropy value.