Geodesic
Generalized Hake property for integrals of Henstock type
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 9-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A Henstock–Kurzweil type integral with respect to an abstract derivation basis in a topological space is considered. It is proved that under certain assumption put on the basis, a generalized Hake property holds true for this integral. 
@article{VMUMM_2013_6_a1,
     author = {V. A. Skvortsov and F. Tulone},
     title = {Generalized {Hake} property for integrals of {Henstock} type},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {9--13},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a1/}
}
TY  - JOUR
AU  - V. A. Skvortsov
AU  - F. Tulone
TI  - Generalized Hake property for integrals of Henstock type
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2013
SP  - 9
EP  - 13
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a1/
LA  - ru
ID  - VMUMM_2013_6_a1
ER  - 
%0 Journal Article
%A V. A. Skvortsov
%A F. Tulone
%T Generalized Hake property for integrals of Henstock type
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2013
%P 9-13
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a1/
%G ru
%F VMUMM_2013_6_a1
V. A. Skvortsov; F. Tulone. Generalized Hake property for integrals of Henstock type. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 9-13. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a1/

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

[2] Lukashenko T.P., Skvortsov V.A., Solodov A.P., Obobschennye integraly, URSS, M., 2010

[3] Faure C-A., Mawhin J., “The Hake's property for some integrals over multidimensional intervals”, Real Anal. Exchange, 20:2 (1994/95), 622–630 | MR

[4] Kurzweil J., Jarnik J., “Differentiability and integrability in $n$ dimensions with respect to $\alpha$-regular intervals”, Results Math., 21 (1992), 138–151 | DOI | MR

[5] Math. Notes, 78:2 (2005), 228–233 | DOI | DOI | MR

[6] Ostaszewski K.M., Henstock integration in the plane, Mem. AMS, 63, no. 353, 1986 | MR

[7] Thomson B.S., “Derivation bases on the real line”, Real Anal. Exchange, 8:1 (1982/83), 67–207 ; 2, 278–442 | MR | MR

[8] Ahmed S.I., Pfeffer W.F., “A Riemann integral in a locally compact Hausdorff space”, Austral. Math. Soc. (Ser. A), 41 (1986), 115–137 | DOI | MR

[9] Skvortsov V.A., Tulone F., “$\mathcal P$-ichnyi integral Khenstoka v teorii ryadov po sistemam kharakterov nulmernykh grupp”, Vestn. Mosk. un-ta. Matem. Mekhan., 2006, no. 1, 25–29

[10] Skvortsov V.A., Tulone F., “Integral khenstokovskogo tipa na kompaktnom nulmernom metricheskom prostranstve i predstavlenie kvazimery”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 2, 11–17

[11] Lee P.Y., Výborný R., The integral: an easy approach after Kurzweil and Henstock, Austral. Math. Soc. Lect. Ser., 14, Cambridge Univ. Press, Cambridge, 2000 | MR