Variational measures in the theory of the integration in ℝ m

Luisa Di Piazza

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 1, page 95-110
  • ISSN: 0011-4642

Abstract

top
We study properties of variational measures associated with certain conditionally convergent integrals in ℝ m . In particular we give a full descriptive characterization of these integrals.

How to cite

top

Di Piazza, Luisa. "Variational measures in the theory of the integration in $\mathbb {R}^m$." Czechoslovak Mathematical Journal 51.1 (2001): 95-110. <http://eudml.org/doc/30617>.

@article{DiPiazza2001,
abstract = {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.},
author = {Di Piazza, Luisa},
journal = {Czechoslovak Mathematical Journal},
keywords = {variational measures and derivates of set functions; Riemann generalized integrals; variational measures and derivates of set functions; Riemann generalized integrals; Henstock-Kurzweil integral},
language = {eng},
number = {1},
pages = {95-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variational measures in the theory of the integration in $\mathbb \{R\}^m$},
url = {http://eudml.org/doc/30617},
volume = {51},
year = {2001},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 95
EP - 110
AB - 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.
LA - eng
KW - variational measures and derivates of set functions; Riemann generalized integrals; variational measures and derivates of set functions; Riemann generalized integrals; Henstock-Kurzweil integral
UR - http://eudml.org/doc/30617
ER -

References

top
  1. Essential variation. Measure Theory Oberwolfach 1981, Lecture Notes in Math. No. 945, Springer-Verlag, Berlin, 1981, pp. 187–193. (1981) MR0675282
  2. 10.1006/jmaa.1998.5982, J. Math. Anal. Appl. 224 (1998), 22–33. (1998) MR1632942DOI10.1006/jmaa.1998.5982
  3. 10.1007/BF02342334, Anal. Math. 22 (1996), 3–12. (1996) MR1384345DOI10.1007/BF02342334
  4. A new full descriptive characterization of Denjoy-Perron integral, Real Anal. Exchange 21 (1995–96), 656–663. (1995–96) MR1407278
  5. 10.1006/jmaa.1997.5804, J. Math. Anal. Appl. 222 (1998), 64–78. (1998) MR1623859DOI10.1006/jmaa.1997.5804
  6. Perron-type integration on n -dimensional intervals and its properties, Czechoslovak Math. J. 45 (120) (1995), 79–106. (1995) MR1314532
  7. 10.1007/BF03323075, Results Math. 21 (1992), 138–151. (1992) MR1146639DOI10.1007/BF03323075
  8. Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields, Czechoslovak Math. J. 31 (106) (1981), 614–632. (1981) Zbl0562.26004MR0631606
  9. Unified integration, Academic Press, New York, 1983. (1983) Zbl0551.28001MR0740710
  10. Henstock integration in the plane, Mem. Amer. Math. Soc. 253 (1986). (1986) Zbl0596.26005MR0856159
  11. The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. (1993) Zbl0804.26005MR1268404
  12. On variation of functions of one real variable, Comment. Math. Univ. Carolin. 38 (1997), 61–71. (1997) MR1455470
  13. On additive continuous functions of figures, Rend. Instit. Mat. Univ. Trieste, suppl. 29 (1998), 115–133. (1998) Zbl0921.26008MR1696024
  14. Real and complex analysis, McGraw-Hill, New York, 1987. (1987) Zbl0925.00005MR0924157
  15. Theory of the integral, Dover, New York, 1964. (1964) MR0167578
  16. Derivates of intervals functions, Mem. Amer. Math. Soc. 452 (1991). (1991) MR1078198

Citations in EuDML Documents

top
  1. Diana Caponetti, On the σ -finiteness of a variational measure
  2. Donatella Bongiorno, Luisa Di Piazza, Valentin A. Skvortsov, Variational measures related to local systems and the Ward property of 𝒫 -adic path bases
  3. Sokol Bush Kaliaj, New extension of the variational McShane integral of vector-valued functions
  4. Sokol Bush Kaliaj, Some remarks on descriptive characterizations of the strong McShane integral
  5. Tuo-Yeong Lee, Some full characterizations of the strong McShane integral
  6. Tuo-Yeong Lee, A measure-theoretic characterization of the Henstock-Kurzweil integral revisited

NotesEmbed ?

top

You must be logged in to post comments.