Asymptotically Mean Stationary Measures
作者： Robert M. Gray , J. C. Kieffer
关键词: Invertible matrix 、 Transformation (function) 、 Probability space 、 Ergodic theory 、 Mean value theorem (divided differences) 、 Mathematical analysis 、 Stationary measures 、 Mathematics 、 Measure (mathematics) 、 Stationary ergodic process 、 Applied mathematics
摘要: Numerous properties are developed of measures that asymptotically mean stationary with respect to a possibly nonsingular and noninvertible measurable transformation on probability space. In particular, several necessary sufficient conditions for the measure satisfy ergodic theorem given, an asymptotic form Radon-Nikodym dominated is developed, behavior resulting derivatives described. As application we prove Shannon-McMillan-Breiman case considered. Several examples given illustrate results.
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