Geodesic
Mean Distality and Tightness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 312-319

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A relationship between the entropy invariant and a certain property of topological dynamical systems with a finite invariant measure $\mu$ is studied. This property means that, after removing a $\mu$-null set, there are no distinct mean proximal points in the system (a pair $x,y$ is mean proximal with respect to a homeomorphism $T$ of a compact metric space with a metric $d$ if $\varlimsup\frac1{2n+1}\sum^n_{-n} d(T^ix, T^iy) = 0$). 
@article{TM_2004_244_a13,
     author = {D. Ornstein and V. Weiss},
     title = {Mean {Distality} and {Tightness}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {312--319},
     publisher = {mathdoc},
     volume = {244},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_244_a13/}
}
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D. Ornstein; V. Weiss. Mean Distality and Tightness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 312-319. http://geodesic.mathdoc.fr/item/TM_2004_244_a13/