The discrete parts of approximately decidable sets in Euclidean spaces

It is shown that the classes of discrete parts, A ∩ ?^k, of approximately resp. weakly decidable subsets of Euclidean spaces, A ? ?^k, coincide and are equal to the class of ω‐r. e. sets which is well‐known as the first transfinite level in Ershov's hierarchy exhausting Δ⁰₂.