''t'' periodic period ''q'' thus cannot ergodic interval ''i'' length ''a'' ''a'' ''q'' orbit ''t'' union ''i'' ''t'' ''i'' ''t'' sup ''q'' sup ''i'' contains image ''i'' number applications ''t'' ''t'' invariant mod set union ''q'' intervals length ''a'' hence measure ''qa'' strictly nbsp let ''g'' compact abelian group '' '' normalized haar measure ''t'' group automorphism ''g'' let ''g'' pontryagin dual group
Formal science Mathematics Pure mathematics Probability theory Ergodic theory