Asymptotic expansion in measure and strong ergodicity
Keyword(s):
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.
2011 ◽
Vol 04
(03)
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pp. 545-557
1990 ◽
Vol 431
(1883)
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pp. 509-518
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1986 ◽
Vol 44
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pp. 382-383
1979 ◽
Vol 10
(3)
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pp. 145-151
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1998 ◽
Vol 5
(1)
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pp. 72A-72A
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2007 ◽
Vol 2007
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pp. 158-159
2018 ◽
Vol 17
(2)
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pp. 55-65
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