Rigidity

An ergodic ℤ d -action α by automorphisms of a compact, abelian group X usually has many distinct non-atomic, invariant, ergodic probability measures. For example, if d ≥ 1, and if α is the shift-action (2.1) of ℤ d on $$ X = {G^{{{\mathbb{Z}^2}}}} \mu = {v^{{{\mathbb{Z}^d}}}} \mu ' = v{'^{{{\mathbb... View More