Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 625-637
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
Classification : 26A39, 26B99, 28A12
Keywords: generalized absolute continuity; Henstock-Kurzweil integral
@article{CMJ_2005_55_3_a4,
     author = {Tuo-Yeong, Lee},
     title = {Some full descriptive characterizations of the {Henstock-Kurzweil} integral in the {Euclidean} space},
     journal = {Czechoslovak Mathematical Journal},
     pages = {625--637},
     year = {2005},
     volume = {55},
     number = {3},
     mrnumber = {2153087},
     zbl = {1081.26008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a4/}
}
TY  - JOUR
AU  - Tuo-Yeong, Lee
TI  - Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 625
EP  - 637
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a4/
LA  - en
ID  - CMJ_2005_55_3_a4
ER  - 
%0 Journal Article
%A Tuo-Yeong, Lee
%T Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
%J Czechoslovak Mathematical Journal
%D 2005
%P 625-637
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a4/
%G en
%F CMJ_2005_55_3_a4
Tuo-Yeong, Lee. Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 625-637. http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a4/

[1] A. M.  Bruckner, J. B.  Bruckner and B. S.  Thomson: Real Analysis. Prentice-Hall, , 1997.

[2] Z.  Buczolich: Henstock integrable functions are Lebesgue integrable on a portion. Proc. American Math. Soc. 111 (1991), 127–129. | DOI | MR | Zbl

[3] Claude-Alain  Faure: A descriptive definition of some multidimensional gauge integrals. Czechoslovak Math.  J. 45 (1995), 549–562. | MR

[4] R. A.  Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics Vol. 4. AMS, Providence, 1994. | MR

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

[6] W. B.  Jurkat and R. W.  Knizia: A characterization of multi-dimensional Perron integrals and the fundamental theorem. Canad.  J. Math. 43 (1991), 526–539. | DOI | MR

[7] J.  Kurzweil and J.  Jarník: Equiintegrability and controlled convergence of Perron-type integrable functions. Real Anal. Exchange 17 (1991/92), 110–139. | MR

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

[9] Lee Peng Yee and Ng Wee Leng: The Radon-Nikodým theorem for the Henstock integral in Euclidean space. Real Anal. Exchange 22 (1996/97), 677–687. | MR

[10] Lee Peng Yee and Rudolf Výborný: The integral, an easy approach after Kurzweil and Henstock. Australian Mathematical Society Lecture Series  14, Cambridge University Press, Cambridge, 2000. | MR

[11] Lee Tuo Yeong, Chew Tuan Seng and Lee Peng Yee: On Henstock integrability in Euclidean spaces. Real Anal. Exchange 22 (1996/97), 382–389. | MR

[12] Lee Tuo Yeong: A full characterization of multipliers for the strong $\rho $-integral in the Euclidean space. Czechoslovak Math.  J. 54 (2004), 657–674. | DOI | MR

[13] Lee Tuo Yeong: The sharp Riesz-type definition for the Henstock-Kurzweil integral. Real Anal. Exchange 28 (2002/2003), 55–70. | MR

[14] Lee Tuo Yeong: A full descriptive definition of the Henstock-Kurzweil integral in the Euclidean space. Proc. London Math. Soc. 87 (2003), 677–700. | MR | Zbl

[15] Lee Tuo Yeong: Some full characterizations of the strong McShane integral. Math. Bohem. 129 (2004), 305–312. | MR | Zbl

[16] Lu Jitan and Lee Peng Yee: The primitives of Henstock integrable functions in Euclidean space. Bull. London Math. Soc. 31 (1999), 173–180. | DOI | MR

[17] S.  Saks: Theory of the Integral, 2nd edition. Stechert & Co., New York, 1964. | MR