Geodesic
The Helly problem and best approximation in a space of continuous functions
Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 623-637.

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Equivalence is verified between the Helly problem in the theory of moments and the problem of best approximation by elements of subspaces of finite defect. The existence and uniqueness conditions for the solution of these problems in a space of continuous functions are investigated. 
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A. L. Garkavi. The Helly problem and best approximation in a space of continuous functions. Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 623-637. http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a5/

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