The linearity of metric projection operator for subspaces of L_p spaces / Yu. Yu. Druzhinin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 30-36 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 28-33].

Let Y be a Chebyshev subspace of a Banach space X. Then the single-valued metric projection operator P_Y:X\to Y taking each x\in X to the nearest element y\in Y is well defined. Let M be an arbitrary set and \mu be a \sigma-finite measure on some \sigma-algebra \Sigma of subsets of M. We give a description of Chebyshev subspaces Y\subset L_p(M,\Sigma,\mu) with finite dimension and finite codimension the operator P_Y is linear for.

Key words: metric projection, Chebyshev subspace, quasiorthogonal set, linearity criterion.