Geodesic
Applications of anticompact sets to analogs of Denjoy--Young--Saks and Lebesgue theorems
Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 115-122

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

We consider the problem of transfer of the Denjoy–Young–Saks theorem on derivates to infinite-dimensional Banach spaces and the problem of nondifferentiability of indefinite Pettis integral in infinite-dimensional Banach spaces. Our approach is based on the concept of an anticompact set proposed by us earlier. We prove an analog of the Denjoy–Young–Saks theorem on derivates in Banach spaces which have anticompact sets. Also in such spaces we obtain an analog of the Lebesgue theorem. This result states that each indefinite Pettis integral is differentiable almost everywhere in the topology of special Hilbert space generated by some anticompact set in the original space. 
@article{EMJ_2015_6_1_a8,
     author = {F. S. Stonyakin},
     title = {Applications of anticompact sets to analogs of {Denjoy--Young--Saks} and {Lebesgue} theorems},
     journal = {Eurasian mathematical journal},
     pages = {115--122},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a8/}
}
TY  - JOUR
AU  - F. S. Stonyakin
TI  - Applications of anticompact sets to analogs of Denjoy--Young--Saks and Lebesgue theorems
JO  - Eurasian mathematical journal
PY  - 2015
SP  - 115
EP  - 122
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a8/
LA  - en
ID  - EMJ_2015_6_1_a8
ER  - 
%0 Journal Article
%A F. S. Stonyakin
%T Applications of anticompact sets to analogs of Denjoy--Young--Saks and Lebesgue theorems
%J Eurasian mathematical journal
%D 2015
%P 115-122
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a8/
%G en
%F EMJ_2015_6_1_a8
F. S. Stonyakin. Applications of anticompact sets to analogs of Denjoy--Young--Saks and Lebesgue theorems. Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 115-122. http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a8/