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We generalize Berg's notion of quasi-disjointness to actions of countablegroups and prove that every measurably distal system is quasi-disjoint fromevery measure preserving system. As a corollary we obtain easy to checknecessary and sufficient conditions for two systems to be disjoint, providedone of them is measurably distal. We also obtain a Wiener--Wintner type theoremfor countable amenable groups with distal weights and applications to weightedmultiple ergodic averages and multiple recurrence.

Disjointness for measurably distal group actions and applications