Geodesic
$2$-Chebyshev Subspaces in the Spaces~$L_1$ and~$C$
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 819-831

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The $2$-uniqueness subspaces and the finite-dimensional $2$-Chebyshev subspaces of the space $C$ of functions continuous on a Hausdorff compact set and of the space $L_1$ of functions Lebesgue integrable on a set of $\sigma$-finite measure are described. These descriptions are analogs of the well-known Haar and Phelps theorems for ordinary Chebyshev subspaces.
Keywords: Banach space, Hilbert space, $2$-Chebyshev subspace, $2$-uniqueness subspace, $2$-existence subspace, the space $L_1$ of Lebesgue integrable functions. 
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     author = {P. A. Borodin},
     title = {$2${-Chebyshev} {Subspaces} in the {Spaces~}$L_1$ and~$C$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {819--831},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a2/}
}
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P. A. Borodin. $2$-Chebyshev Subspaces in the Spaces~$L_1$ and~$C$. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 819-831. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a2/