For minimal abelian group actions, frequent (m+1)-stability is equivalent to almost m-to-one maximal equicontinuous factors, and diam-mean (m+1)-equicontinuity to almost surely m-to-one factors.
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Multivariate Frequent Stability and Diam-Mean Equicontinuity
For minimal abelian group actions, frequent (m+1)-stability is equivalent to almost m-to-one maximal equicontinuous factors, and diam-mean (m+1)-equicontinuity to almost surely m-to-one factors.