Geodesic
On Korovkin type theorem in the space of locally integrable functions
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 45-53.

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It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space $L_{p,w}({\mathrm loc})$ does not hold in all this space and is satisfied only on some subspace.
Classification : 41A25, 41A36, 41A65
Keywords: linear positive operators; Korovkin type theorem; weighted $L_p({\mathrm loc})$ spaces 
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     title = {On {Korovkin} type theorem in the space of locally integrable functions},
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Gadjiev, A. D.; Efendiyev, R. O.; Ibikli, E. On Korovkin type theorem in the space of locally integrable functions. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 45-53. http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a3/