Geodesic
Pettis integrability of Stone transforms
Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 238-253 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $f$ be a bounded Pettis integrable function ranging in a Banach space $X$ (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform of $f$ and relate this problem to the regular oscillation condition for the family of functions $\{x^*f:x^*\in B(X^*)\}$, where $B(X^*)$ is the unit ball in $X^*$. 
@article{MZM_1996_60_2_a6,
     author = {V. I. Rybakov},
     title = {Pettis integrability of {Stone} transforms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {238--253},
     year = {1996},
     volume = {60},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/}
}
TY  - JOUR
AU  - V. I. Rybakov
TI  - Pettis integrability of Stone transforms
JO  - Matematičeskie zametki
PY  - 1996
SP  - 238
EP  - 253
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/
LA  - ru
ID  - MZM_1996_60_2_a6
ER  - 
%0 Journal Article
%A V. I. Rybakov
%T Pettis integrability of Stone transforms
%J Matematičeskie zametki
%D 1996
%P 238-253
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/
%G ru
%F MZM_1996_60_2_a6
V. I. Rybakov. Pettis integrability of Stone transforms. Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 238-253. http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/

[1] Talangrand M., Pettis integral and measure theory, Amer. Math. Soc. Memoirs, 307, 1984

[2] Sentilles D., Wheeler R., “Pettis integration via the Stonian transform”, Pacific J. Math., 107:2 (1983), 473–495 | MR

[3] Sazonov V. V., “O sovershennykh merakh”, Izv. AN SSSR. Ser. matem., 26:3 (1962), 391–414 | MR

[4] Flemlin D., Talagrand M., “A decomposition theorem for additive set-functions, with applications to Pettis integrals and ergodic means”, Math. Z., 168 (1979), 117–142 | DOI | MR

[5] Ghoussoub N., Godefroy G., Maurey B., Schachermayer W., Some topological and geometrical structures in Banach spaces, Amer. Math. Soc. Memoirs, 378, 1987 | Zbl