Geodesic
Variational measures in the theory of the integration in $\mathbb R^m$
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 95-110 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study properties of variational measures associated with certain conditionally convergent integrals in ${\mathbb R}^m$. In particular we give a full descriptive characterization of these integrals.
We study properties of variational measures associated with certain conditionally convergent integrals in ${\mathbb R}^m$. In particular we give a full descriptive characterization of these integrals.
Classification : 26A39, 26A45, 28A15
Keywords: variational measures and derivates of set functions; Riemann generalized integrals 
@article{CMJ_2001_51_1_a8,
     author = {Di Piazza, Luisa},
     title = {Variational measures in the theory of the integration in $\mathbb R^m$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {95--110},
     year = {2001},
     volume = {51},
     number = {1},
     mrnumber = {1814635},
     zbl = {1079.28500},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a8/}
}
TY  - JOUR
AU  - Di Piazza, Luisa
TI  - Variational measures in the theory of the integration in $\mathbb R^m$
JO  - Czechoslovak Mathematical Journal
PY  - 2001
SP  - 95
EP  - 110
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a8/
LA  - en
ID  - CMJ_2001_51_1_a8
ER  - 
%0 Journal Article
%A Di Piazza, Luisa
%T Variational measures in the theory of the integration in $\mathbb R^m$
%J Czechoslovak Mathematical Journal
%D 2001
%P 95-110
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a8/
%G en
%F CMJ_2001_51_1_a8
Di Piazza, Luisa. Variational measures in the theory of the integration in $\mathbb R^m$. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 95-110. http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a8/

[1] B. Bongiorno: Essential variation. Measure Theory Oberwolfach 1981. Lecture Notes in Math. No. 945, Springer-Verlag, Berlin, 1981, pp. 187–193. | MR

[BDP] B. Bongiorno, L. Di Piazza and D. Preiss: Infinite variation and derivates in ${R}^m$. J. Math. Anal. Appl. 224 (1998), 22–33. | DOI | MR

[3] B. Bongiorno, L. Di Piazza and V. Skvortsov: The essential variation of a function and some convergence theorems. Anal. Math. 22 (1996), 3–12. | DOI | MR

[BDS] B. Bongiorno, L. Di Piazza and V. Skvortsov: A new full descriptive characterization of Denjoy-Perron integral. Real Anal. Exchange 21 (1995–96), 656–663. | MR

[2] Z. Buczolich and W. F. Pfeffer: On absolute continuity. J. Math. Anal. Appl. 222 (1998), 64–78. | DOI | MR

[4] J. Jarník and J. Kurzweil: Perron-type integration on $n$-dimensional intervals and its properties. Czechoslovak Math. J. 45 (120) (1995), 79–106. | MR

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

[6] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields. Czechoslovak Math. J. 31 (106) (1981), 614–632. | MR | Zbl

[Mc] E. J. McShane: Unified integration. Academic Press, New York, 1983. | MR | Zbl

[O] K. M. Ostaszewski: Henstock integration in the plane. Mem. Amer. Math. Soc. 253 (1986). | MR | Zbl

[7] W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Univ. Press, Cambridge, 1993. | MR | Zbl

[P] W. F. Pfeffer: On variation of functions of one real variable. Comment. Math. Univ. Carolin. 38 (1997), 61–71. | MR

[8] W. F. Pfeffer: On additive continuous functions of figures. Rend. Instit. Mat. Univ. Trieste, suppl. 29 (1998), 115–133. | MR | Zbl

[9] W. Rudin: Real and complex analysis. McGraw-Hill, New York, 1987. | MR | Zbl

[10] S. Saks: Theory of the integral. Dover, New York, 1964. | MR

[11] B. S. Thomson: Derivates of intervals functions. Mem. Amer. Math. Soc. 452 (1991). | MR