Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 491-498
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K. N. Lungu. Best approximations by rational functions with respect to the Hausdorff distance. Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 491-498. http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a2/
@article{MZM_1972_11_5_a2,
author = {K. N. Lungu},
title = {Best approximations by rational functions with respect to the {Hausdorff} distance},
journal = {Matemati\v{c}eskie zametki},
pages = {491--498},
year = {1972},
volume = {11},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a2/}
}
TY - JOUR
AU - K. N. Lungu
TI - Best approximations by rational functions with respect to the Hausdorff distance
JO - Matematičeskie zametki
PY - 1972
SP - 491
EP - 498
VL - 11
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a2/
LA - ru
ID - MZM_1972_11_5_a2
ER -
%0 Journal Article
%A K. N. Lungu
%T Best approximations by rational functions with respect to the Hausdorff distance
%J Matematičeskie zametki
%D 1972
%P 491-498
%V 11
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a2/
%G ru
%F MZM_1972_11_5_a2
Inverse theorems on the best approximations of plane sets in a Hausdorff metric by means of rational functions are cited. It is shown, among other things, that if $R_{n,r}(F,[a,b])=o(1/n)$, then there exists a set $P\subset[a,b]$ of complete measure over which $F$ constitutes a single-valued function.
