Geodesic
On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 221-228

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Conditions for the constants of best approximation in the metric of the spaces $L^p(B)$ to be continuous or semicontinuous as functions of the center of a ball $B$ of fixed radius in a metric space with Borel measure are studied.
Keywords: metric measure space, best approximations by constants. 
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     author = {I. N. Katkovskaya and V. G. Krotov},
     title = {On the {Continuity} of {Best} {Approximations} by {Constants} on {Balls} in {Metric} {Measure} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {221--228},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/}
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I. N. Katkovskaya; V. G. Krotov. On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 221-228. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/