On Riemann-type definition for the wide Denjoy integral

Piotr Sworowski

Rendiconti del Seminario Matematico della Università di Padova (2011)

  • Volume: 126, page 175-200
  • ISSN: 0041-8994

How to cite

top

Sworowski, Piotr. "On Riemann-type definition for the wide Denjoy integral." Rendiconti del Seminario Matematico della Università di Padova 126 (2011): 175-200. <http://eudml.org/doc/240110>.

@article{Sworowski2011,
author = {Sworowski, Piotr},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {175-200},
publisher = {Seminario Matematico of the University of Padua},
title = {On Riemann-type definition for the wide Denjoy integral},
url = {http://eudml.org/doc/240110},
volume = {126},
year = {2011},
}

TY - JOUR
AU - Sworowski, Piotr
TI - On Riemann-type definition for the wide Denjoy integral
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2011
PB - Seminario Matematico of the University of Padua
VL - 126
SP - 175
EP - 200
LA - eng
UR - http://eudml.org/doc/240110
ER -

References

top
  1. [1] B. Bongiorno - L. Di Piazza - V. A. Skvortsov, On dyadic integrals and some other integrals associated with local systems, Journal of Mathematical Analysis and Applications, 271 (2) (2002), pp. 506–524. Zbl1010.26006MR1923649
  2. [2] A. Denjoy, Une extension de l'intégrale de M. Lebesgue, Comptes Rendus De l'Académie des Sciences, 154 (1912), pp. 859–862. Zbl43.0360.01JFM43.0360.01
  3. [3] A. Denjoy, Sur la dérivation et son calcul inverse, Comptes Rendus De l'Académie des Sciences, 162 (1916), pp. 377–380. Zbl46.0381.02JFM46.0381.02
  4. [4] V. Ene, On Borel measurable functions that are V B G and 𝒩 , Real Analysis Exchange, 22 (2) (1996/97), pp. 688–695. Zbl0942.26019MR1460981
  5. [5] V. Ene, A study of some general integrals that contains the wide Denjoy integral, Real Analysis Exchange, 26 (1) (2000/01), pp. 51–100. Zbl1010.26007MR1825497
  6. [6] R. Henstock, A new descriptive definition of the Ward integral, The Journal of the London Mathematical Society, 35 (1960), pp. 43–48. Zbl0095.04504MR110780
  7. [7] R. Henstock, Definitions of Riemann type of the variational integrals, Proceedings of the London Mathematical Society, Third Series, 11 (1961), pp. 402–418. Zbl0099.27402MR132147
  8. [8] R. Henstock, Linear Analysis, Butterworths, London, 1967. Zbl0172.39001MR419707
  9. [9] R. Henstock, The variation on the real line, Proceedings of the Royal Irish Academy. Section A, 79 (1) (1979), pp. 1–10. Zbl0358.26005MR541680
  10. [10] A. Khintchine, Sur une extension de l'intégrale de M. Denjoy, Comptes Rendus de l'Académie des Sciences, 162 (1916), pp. 287–291. Zbl46.0381.01JFM46.0381.01
  11. [11] J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Mathematical Journal, 7 (82) (1957), pp. 418–449. Zbl0090.30002MR111875
  12. [12] Lee C.-M., On Baire one Darboux functions with Lusin’s condition , Real Analysis Exchange, 7 (1) (1981/82), pp. 61–64. Zbl0531.26004MR646637
  13. [13] Lee T.-Y. - Lee P.-Y., The Kubota integral II, Mathematica Japonica, 42 (2) (1995), pp. 257–263. Zbl0844.26007MR1356385
  14. [14] N. N. Lusin, Sur les propriétés de l'intégrale de M. Denjoy, Comptes Rendus de l'Académie des Sciences, 155 (1912), pp. 1475–1477. Zbl43.0360.03JFM43.0360.03
  15. [15] W. Poreda - E. Wagner-Bojakowska - W. Wilczyński, A category analogue of the density topology, Fundamenta Mathematicae, 125 (2) (1985), pp. 167–173. Zbl0613.26002MR813753
  16. [16] S. Saks, Theory of Integral, G. E. Stechert, New York, 1937. Zbl0017.30004JFM63.0183.05
  17. [17] D. N. Sarkhel - A. K. De, The proximally continuous integrals, Journal of the Australian Mathematical Society (Series A), 31 (1) (1981), pp. 26–45. Zbl0477.26002MR622811
  18. [18] D. N. Sarkhel - A. B. Kar, [PVB] functions and integration, Journal of the Australian Mathematical Society (Series A), 36 (3) (1984), pp. 335–353. Zbl0547.26009MR733906
  19. [19] B. Soedijono - Lee P.-Y., The Kubota integral, Mathematica Japonica, 36 (2) (1991), pp. 263–270. Zbl0726.26006MR1095739
  20. [20] P. Sworowski, An answer to some questions of Ene, Real Analysis Exchange, 30 (1) (2004/05), pp. 183–192. Zbl1060.26011MR2127524
  21. [21] P. Sworowski, Some Kurzweil-Henstock-type integrals and the wide Denjoy integral, Czechoslovak Mathematical Journal, 57 (132) (1) (2007), pp. 419–434. Zbl1174.26309MR2309975
  22. [22] P. Sworowski, On the approximately continuous Foran integral: completing our chart, Real Analysis Exchange, 33 (1) (2007/08), pp. 29–40. Zbl1154.26010MR2402861
  23. [23] B. S. Thomson, Derivation bases on the real line. I, Real Analysis Exchange, 8 (1) (1982/83), pp. 67–207. Zbl0525.26002MR694507
  24. [24] B. S. Thomson, Derivation bases on the real line. II, Real Analysis Exchange, 8 (2) (1982/83), pp. 278–442. Zbl0525.26003MR700194
  25. [25] B. S. Thomson, Real Functions, Lecture Notes in Mathematics, 1170 (Springer, Berlin, 1985). Zbl0581.26001MR818744

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.