Abstract
Let ( Σ, ρ) denote the one-sided symbolic space (with two symbols), σ the shift on Σ, A(·) the set of almost periodic points and R(·) the set of recurrent points. It is shown that there exists an uncountable set T with T⊂R(σ)−A(σ) such that σ : T→ T is uniquely ergodic.
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