Abstract
An ergodic Zd-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 Zd on X = G Z 2 , where G is a nontrivial, compact, abelian group, then there exist uncountably many distinct, a-invariant, mixing probability measures on X:
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