Discrete spectrum for amenable group actions
Keyword(s):
<p style='text-indent:20px;'>In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions.</p><p style='text-indent:20px;'>We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean.</p>
2018 ◽
Vol 38
(4)
◽
pp. 1657-1667
◽
2019 ◽
Vol 41
(2)
◽
pp. 494-533
◽
1993 ◽
Vol 03
(04)
◽
pp. 1045-1049
2018 ◽
Vol 38
(9)
◽
pp. 4467-4482
Keyword(s):
1998 ◽
Vol 18
(5)
◽
pp. 1049-1073
◽