On Riemann-type definition for the wide Denjoy integral
Rendiconti del Seminario Matematico della Università di Padova, Tome 126 (2011), pp. 175-200.
@article{RSMUP_2011__126__175_0,
     author = {Sworowski, Piotr},
     title = {On {Riemann-type} definition for the wide {Denjoy} integral},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {175--200},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {126},
     year = {2011},
     mrnumber = {2918205},
     zbl = {1232.26007},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2011__126__175_0/}
}
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
SP  - 175
EP  - 200
VL  - 126
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_2011__126__175_0/
LA  - en
ID  - RSMUP_2011__126__175_0
ER  - 
%0 Journal Article
%A Sworowski, Piotr
%T On Riemann-type definition for the wide Denjoy integral
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2011
%P 175-200
%V 126
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_2011__126__175_0/
%G en
%F RSMUP_2011__126__175_0
Sworowski, Piotr. On Riemann-type definition for the wide Denjoy integral. Rendiconti del Seminario Matematico della Università di Padova, Tome 126 (2011), pp. 175-200. http://www.numdam.org/item/RSMUP_2011__126__175_0/

[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. | MR | Zbl

[2] A. Denjoy, Une extension de l'intégrale de M. Lebesgue, Comptes Rendus De l'Académie des Sciences, 154 (1912), pp. 859-862. | JFM

[3] A. Denjoy, Sur la dérivation et son calcul inverse, Comptes Rendus De l'Académie des Sciences, 162 (1916), pp. 377-380. | JFM

[4] V. Ene, On Borel measurable functions that are VBG and 𝒩 , Real Analysis Exchange, 22 (2) (1996/97), pp. 688-695. | MR | Zbl

[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. | MR | Zbl

[6] R. Henstock, A new descriptive definition of the Ward integral, The Journal of the London Mathematical Society, 35 (1960), pp. 43-48. | MR | Zbl

[7] R. Henstock, Definitions of Riemann type of the variational integrals, Proceedings of the London Mathematical Society, Third Series, 11 (1961), pp. 402-418. | MR | Zbl

[8] R. Henstock, Linear Analysis, Butterworths, London, 1967. | MR | Zbl

[9] R. Henstock, The variation on the real line, Proceedings of the Royal Irish Academy. Section A, 79 (1) (1979), pp. 1-10. | MR | Zbl

[10] A. Khintchine, Sur une extension de l'intégrale de M. Denjoy, Comptes Rendus de l'Académie des Sciences, 162 (1916), pp. 287-291. | JFM

[11] J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Mathematical Journal, 7 (82) (1957), pp. 418-449. | MR | Zbl

[12] Lee C.-M., On Baire one Darboux functions with Lusin's condition 𝒩 , Real Analysis Exchange, 7 (1) (1981/82), pp. 61-64. | MR | Zbl

[13] Lee T.-Y. - Lee P.-Y., The Kubota integral II, Mathematica Japonica, 42 (2) (1995), pp. 257-263. | MR | Zbl

[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. | JFM

[15] W. Poreda - E. Wagner-Bojakowska - W. Wilczyński, A category analogue of the density topology, Fundamenta Mathematicae, 125 (2) (1985), pp. 167-173. | MR | Zbl

[16] S. Saks, Theory of Integral, G. E. Stechert, New York, 1937. | JFM | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[19] B. Soedijono - Lee P.-Y., The Kubota integral, Mathematica Japonica, 36 (2) (1991), pp. 263-270. | MR | Zbl

[20] P. Sworowski, An answer to some questions of Ene, Real Analysis Exchange, 30 (1) (2004/05), pp. 183-192. | MR | Zbl

[21] P. Sworowski, Some Kurzweil-Henstock-type integrals and the wide Denjoy integral, Czechoslovak Mathematical Journal, 57 (132) (1) (2007), pp. 419-434. | MR | Zbl

[22] P. Sworowski, On the approximately continuous Foran integral: completing our chart, Real Analysis Exchange, 33 (1) (2007/08), pp. 29-40. | MR | Zbl

[23] B. S. Thomson, Derivation bases on the real line. I, Real Analysis Exchange, 8 (1) (1982/83), pp. 67-207. | MR | Zbl

[24] B. S. Thomson, Derivation bases on the real line. II, Real Analysis Exchange, 8 (2) (1982/83), pp. 278-442. | MR | Zbl

[25] B. S. Thomson, Real Functions, Lecture Notes in Mathematics, 1170 (Springer, Berlin, 1985). | MR | Zbl