Let $\Omega$ be the support of a probability space and of a metric space. If $T:\Omega\to\Omega$ is weakly mixxing, then for every measurable set $AS$ of strictly positive probability, one has $\limsup \delta(T^nSA)=delta(\Omega)$, where $\delta$ denotes the diameter of of a subset of $\Omega$. This results complements a previous one by Rice for strongly mixing transformations.
On Weakly Mixing Transformation on Metric Spaces
SEMPI, Carlo
1985-01-01
Abstract
Let $\Omega$ be the support of a probability space and of a metric space. If $T:\Omega\to\Omega$ is weakly mixxing, then for every measurable set $AS$ of strictly positive probability, one has $\limsup \delta(T^nSA)=delta(\Omega)$, where $\delta$ denotes the diameter of of a subset of $\Omega$. This results complements a previous one by Rice for strongly mixing transformations.File in questo prodotto:
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