Approximation and differential properties of measurable sets
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 401-418
Cet article a éte moissonné depuis 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.
@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/}
}
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/
[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