Geodesic
Differential properties of a measurable function of one real
Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 953-964.

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

This article is concerned with studying the differential properties of a measurable function. It is shown that only three possibilities can be realized in the structure of measurable functions. 
@article{IM2_1970_4_4_a11,
     author = {F. I. Shmidov},
     title = {Differential properties of a measurable function of one real},
     journal = {Izvestiya. Mathematics },
     pages = {953--964},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a11/}
}
TY  - JOUR
AU  - F. I. Shmidov
TI  - Differential properties of a measurable function of one real
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 953
EP  - 964
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a11/
LA  - en
ID  - IM2_1970_4_4_a11
ER  - 
%0 Journal Article
%A F. I. Shmidov
%T Differential properties of a measurable function of one real
%J Izvestiya. Mathematics 
%D 1970
%P 953-964
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a11/
%G en
%F IM2_1970_4_4_a11
F. I. Shmidov. Differential properties of a measurable function of one real. Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 953-964. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a11/

[1] Denjoy A., “Memoire sur la totalisation des nombres derives non-sommables”, Ann. Ecole Norm., 33 (1916), 127–222 | MR

[2] Khinchin A. Ya., “Issledovaniya o stroenii izmerimykh funktsii”, Matem. sb., 31:2 (1923), 265–285 | Zbl

[3] Burkill D., Haslam-Jones U. S., “The derivates und approximative derivates of measurable functions”, Proc. London Math. Soc.(2), 32 (1931), 346–355 | DOI | Zbl

[4] Jarnik V., “Sur les nombres derives approximatifs”, Fundam. math., 22 (1934), 4–16 | Zbl

[5] Shmidov F. I., Differentsialnye svoistva mnozhestv i funktsii, Dissertatsiya, M., 1938

[6] Plamennov I. Ya., “K differentsialnym svoistvam izmerimykh funktsii”, Dokl. AN SSSR, 104:6 (1957), 819–820 | MR

[7] Khoang Tui, “K strukture izmerimykh funktsii”, Dokl. AN SSSR, 126:1 (1959), 37–40 | MR | Zbl

[8] Saks S., Teoriya integrala, IL, M., 1949

[9] Tolstov G. P., “Sur la dérivés approximative exacic”, Matem. sb., 4(46) (1938), 499–504 | Zbl