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MR1107269 (94b:41007) 41A10 (41A50 46E30)
Brown, Lawrence G.; Lucier, Bradley J. Best approximations in $L\sp 1$ are near best in $L\sp p,\ p<1$. Proc. Amer. Math. Soc. 120 (1994), no. 1, 97–100.
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