Nullness is equivalent to polynomial maximal pattern complexity, equicontinuity to bounded pattern complexity, and transitive nonminimal null systems exist with prescribed rigidity and scattering properties.
Hoeffding,Probability inequalities for sums of bounded random variables, J
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Maximal pattern complexity and structure of null systems
Nullness is equivalent to polynomial maximal pattern complexity, equicontinuity to bounded pattern complexity, and transitive nonminimal null systems exist with prescribed rigidity and scattering properties.