Geodesic
Approximation and differential properties of measurable sets
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 401-418 
A. N. Zhdanov; E. A. Sevast'yanov. Approximation and differential properties of measurable sets. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 401-418. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a7/
@article{SM_1984_49_2_a7,
     author = {A. N. Zhdanov and E. A. Sevast'yanov},
     title = {Approximation and differential properties of measurable sets},
     journal = {Sbornik. Mathematics},
     pages = {401--418},
     year = {1984},
     volume = {49},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_2_a7/}
}
TY  - JOUR
AU  - A. N. Zhdanov
AU  - E. A. Sevast'yanov
TI  - Approximation and differential properties of measurable sets
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 401
EP  - 418
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1984_49_2_a7/
LA  - en
ID  - SM_1984_49_2_a7
ER  - 
%0 Journal Article
%A A. N. Zhdanov
%A E. A. Sevast'yanov
%T Approximation and differential properties of measurable sets
%J Sbornik. Mathematics
%D 1984
%P 401-418
%V 49
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1984_49_2_a7/
%G en
%F SM_1984_49_2_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the authors establish approximation properties of measurable sets, which are then applied to study the differential properties of sets connected with the notion of points of density. A refinement of the well-known Lebesgue theorem on points of density of measurable sets is obtained. Bibliography: 7 titles.

[1] Lebeg A., Integrirovanie i otyskanie primitivnykh funktsii, GTTI, M., L., 1934

[2] Luzin N. N., (Pribavlenie k knige A. Lebega [1]),, 290–310

[3] Tolstov G. P., “O tochkakh plotnosti lineinykh izmerimykh mnozhestv”, Matem. sb., 10 (52) (1942), 249–264 | Zbl

[4] Korneichuk N. P., Ekstremalnye zadachi teorii priblizheniya, Nauka, M., 1976 | MR

[5] Newman D. J., “Rational approximation to $|x|$”, Mich. Math. Journ., 11:1 (1964), 11–14 | DOI | MR | Zbl

[6] Sevastyanov E. A., “Nekotorye otsenki proizvodnykh ratsionalnykh funktsii v integralnykh metrikakh”, Matem. zametki, 13:4 (1973), 499–510

[7] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR