Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 715-718
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J. Macys. On the stability of decompositions of the unit distribution function. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 715-718. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a9/
@article{TVP_1969_14_4_a9,
author = {J. Macys},
title = {On the stability of decompositions of the unit distribution function},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {715--718},
year = {1969},
volume = {14},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a9/}
}
TY - JOUR
AU - J. Macys
TI - On the stability of decompositions of the unit distribution function
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 715
EP - 718
VL - 14
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a9/
LA - ru
ID - TVP_1969_14_4_a9
ER -
%0 Journal Article
%A J. Macys
%T On the stability of decompositions of the unit distribution function
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 715-718
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a9/
%G ru
%F TVP_1969_14_4_a9
Let $E$ be the unit distribution function $$ E(x)= \begin{cases} 0,&x\le0 \\ 1,&x>0 \end{cases} $$ and $F=F_1*F_2$ be a distribution function such that in the uniform metric $$ \rho(F,E)\le\varepsilon\le1/4. $$ Let $F_1$ have median 0. We show that $$ \rho(F_1,E)\le\frac{1-\sqrt{1-4\varepsilon}}2. $$ and this estimate can not be improved.
