Geodesic
On a~theorem of A.~G.~Vitushkin
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 178-181

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A. G. Vitushkin in [1] gives a sufficient condition, (in terms of analytic capacity) for the coincidence of algebras $R(E)$ and $C(E)$, $E$ being a compact subset of $\mathbb C$. We present here an easy proof of Vitushkin's theorem. 
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     author = {N. A. Shirokov},
     title = {On a~theorem of {A.~G.~Vitushkin}},
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N. A. Shirokov. On a~theorem of A.~G.~Vitushkin. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 178-181. http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a15/