Recurrence and unique ergodicity

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.