Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
Czechoslovak Mathematical Journal, Tome 46 (1996) no. 1, pp. 1-20 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

DOI : 10.21136/CMJ.1996.127265
Classification : 26A39, 26B15, 26B99
@article{10_21136_CMJ_1996_127265,
     author = {Kurzweil, Jaroslav and Jarn{\'\i}k, Ji\v{r}{\'\i}},
     title = {Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1--20},
     year = {1996},
     volume = {46},
     number = {1},
     doi = {10.21136/CMJ.1996.127265},
     mrnumber = {1371683},
     zbl = {0902.26007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1996.127265/}
}
TY  - JOUR
AU  - Kurzweil, Jaroslav
AU  - Jarník, Jiří
TI  - Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
JO  - Czechoslovak Mathematical Journal
PY  - 1996
SP  - 1
EP  - 20
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1996.127265/
DO  - 10.21136/CMJ.1996.127265
LA  - en
ID  - 10_21136_CMJ_1996_127265
ER  - 
%0 Journal Article
%A Kurzweil, Jaroslav
%A Jarník, Jiří
%T Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
%J Czechoslovak Mathematical Journal
%D 1996
%P 1-20
%V 46
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1996.127265/
%R 10.21136/CMJ.1996.127265
%G en
%F 10_21136_CMJ_1996_127265
Kurzweil, Jaroslav; Jarník, Jiří. Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence. Czechoslovak Mathematical Journal, Tome 46 (1996) no. 1, pp. 1-20. doi: 10.21136/CMJ.1996.127265

[1] R. A. Gordon: A general convergence theorem for nonabsolute integrals. J. London Math. Soc. 44 (1991), 301–309. | MR | Zbl

[2] R. A. Gordon: On the equivalence of two convergence theorems for the Henstock integral. Real Anal. Exchange 18 (1992/93), 261–266. | MR

[3] J. Jarník and J. Kurzweil: Perron-type integration on $n$-dimensional intervals and its properties. Czechosl. Math. J. 45 (1995), 79–106. | MR

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

[5] J. Jarník, J. Kurzweil and Š. Schwabik: On Mawhin’s approach to multiple nonabsolutely convergent integrals. Čas. pěst. mat. 108 (1983), 356–380. | MR

[6] P. Y. Lee and T. S. Chew: A better convergence theorem for Henstock integrals. Bull. London Math. Soc. 17 (1985), 557–564. | DOI | MR

[7] P. Y. Lee and T. S. Chew: A Riesz-type definition of the Denjoy integral. Real Anal. Exchange 11 (1985/86), 221–227. | MR

[8] E. J. McShane: Integration. Princeton University Press, 1947. | MR | Zbl

[9] F. Riesz and B. Sz. Nagy: Vorlesungen über Funktionalanalysis. VEB Deutscher Verlag der Wissenschaften Berlin, 1956. | MR

[10] K. Yosida: Functional Analysis. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. | Zbl

Cité par Sources :