Geodesic
Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures
Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 528-534 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that the definitions of differentiability directions for vector measures in various topologies, namely, the topology of convergence on a system measurable sets, the topology of convergence with respect to semivariation, and the topology of convergence in variation, are generally pairwise nonequivalent. It is also proved that, for measures with values in a Banach space with the Radon–Nikodym property, these definitions are equivalent. 
@article{MZM_2002_72_4_a5,
     author = {V. A. Romanov},
     title = {Nonequivalence of {Various} {Definitions} of {Differentiability} {Directions} for {Vector} {Measures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {528--534},
     year = {2002},
     volume = {72},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a5/}
}
TY  - JOUR
AU  - V. A. Romanov
TI  - Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures
JO  - Matematičeskie zametki
PY  - 2002
SP  - 528
EP  - 534
VL  - 72
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a5/
LA  - ru
ID  - MZM_2002_72_4_a5
ER  - 
%0 Journal Article
%A V. A. Romanov
%T Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures
%J Matematičeskie zametki
%D 2002
%P 528-534
%V 72
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a5/
%G ru
%F MZM_2002_72_4_a5
V. A. Romanov. Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures. Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 528-534. http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a5/

[1] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v beskonechnomerykh prostranstvakh, Nauka, M., 1983

[2] Averbukh V. I., Smolyanov O. G., Fomin S. V., “Obobschennye funktsii i differentsialnye uravneniya v lineinykh prostranstvakh. I: Differentsiruemye mery”, Tr. MMO, 24, URSS, M., 1971, 133–174 | MR | Zbl

[3] Romanov V. A., “O neekvivalentnosti trekh opredelenii nepreryvnykh napravlenii dlya vektornykh mer”, Matem. zametki, 57:2 (1995), 310–312 | MR | Zbl

[4] Romanov V. A., “O razlozhenii mery v lineinom prostranstve v summu $H$-nepreryvnoi i vpolne $H$-razryvnoi mer”, Vestn. MGU. Ser. 1. Matem., mekh., 31:4 (1976), 63–66 | MR | Zbl

[5] Romanov V. A., “Ob $H$-nepreryvnykh merakh v gilbertovom prostranstve”, Vestn. MGU. Ser. 1. Matem., mekh., 32:1 (1977), 81–85 | MR