dc.contributor.author | Skvortsov, Valentin A. | |
dc.contributor.author | Sworowska, Tatiana | |
dc.contributor.author | Sworowski, Piotr | |
dc.contributor.editor | Filipczak, Małgorzata | |
dc.contributor.editor | Wagner-Bojakowska, Elżbieta | |
dc.date.accessioned | 2019-05-21T12:41:02Z | |
dc.date.available | 2019-05-21T12:41:02Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Skvortsov V. A., Sworowska T., Sworowski P., On approximately continuous integrals (a survey), [w:] Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Filipczak M., Wagner-Bojakowska E. (red.), Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013, s. 233-252, doi: 10.18778/7525-971-1.15 | pl_PL |
dc.identifier.isbn | 978-83-7525-971-1 | |
dc.identifier.uri | http://hdl.handle.net/11089/28353 | |
dc.description | The origin of the notion of approximate derivative and, in turn, approximate continuity is closely related with integration theory. The purpose of this chapter is to recollect the lines of development of the theory of generalized integration in connection with approximate continuity. Among the results surveyed, some recent results of the authors are mentioned. | pl_PL |
dc.description.sponsorship | Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00. | pl_PL |
dc.language.iso | en | pl_PL |
dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl_PL |
dc.relation.ispartof | Filipczak M., Wagner-Bojakowska E. (red.), Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013; | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | 26A15 | pl_PL |
dc.subject | 26A24 | pl_PL |
dc.subject | 26A36 | pl_PL |
dc.subject | 26A39 | pl_PL |
dc.subject | 26A42 | pl_PL |
dc.subject | 26A45 | pl_PL |
dc.subject | 26A46 | pl_PL |
dc.subject | 42A10 | pl_PL |
dc.subject | approximately continuous function | pl_PL |
dc.subject | approximate derivative | pl_PL |
dc.subject | approximate Kurzweil–Henstock integral | pl_PL |
dc.subject | Lusin-type integral | pl_PL |
dc.subject | Burkill’s AP-integral | pl_PL |
dc.subject | variational measure | pl_PL |
dc.subject | differential basis | pl_PL |
dc.subject | trigonometric series | pl_PL |
dc.subject | approximate symmetric integral | pl_PL |
dc.title | On approximately continuous integrals (a survey) | pl_PL |
dc.type | Book chapter | pl_PL |
dc.page.number | 233-252 | pl_PL |
dc.contributor.authorAffiliation | Casimirus the Great University, Institute of Mathematics | pl_PL |
dc.contributor.authorAffiliation | Central European Journal of Mathematics | pl_PL |
dc.contributor.authorAffiliation | Casimirus the Great University, Institute of Mathematics | pl_PL |
dc.references | B. Bongiorno, L. Di Piazza, V. Skvortsov, A new full descriptive characterization of Denjoy–Perron integral, Real Anal. Exchange 21 (1995/1996), 656–663. | pl_PL |
dc.references | B. Bongiorno, L. Di Piazza, V. A. Skvortsov, On variational measures related to some bases, J. Math. Anal. Appl. 250 (2000), 533–547. | pl_PL |
dc.references | B. Bongiorno, L. Di Piazza, V. A. Skvortsov, On dyadic integrals and some other integrals associated with local systems, J. Math. Anal. Appl. 271 (2002), 506–524. | pl_PL |
dc.references | D. Bongiorno, L. Di Piazza, V. A. Skvortsov, Variational measures related to local systems and the Ward property of P-adic path bases, Czechoslovak Math. J. 56(31) (2006), 559–578. | pl_PL |
dc.references | P. S. Bullen, The Burkill approximately continuous integral, Journal of the Australian Mathematical Society (Series A) 35 (1983), 236–253. | pl_PL |
dc.references | P. S. Bullen, The Burkill approximately continuous integral. II, Mathematical Chronicle 12 (1983), 93–98. | pl_PL |
dc.references | J. C. Burkill, The approximately continuous Perron integral, Mathematische Zeitschrift 34 (1932), 270–278. | pl_PL |
dc.references | A. Denjoy, Une extension de l’intégrale de M. Lebesgue, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 54 (1912), 859–862. | pl_PL |
dc.references | A. Denjoy, Sur la dérivation et son calcul inverse, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 162 (1916), 377–380. | pl_PL |
dc.references | A. Denjoy, Leçons sur le Calcul des Coefficients d’une Série Trigonométrique, I–IV, Gauthier–Villars, Paris, 1941–1949. | pl_PL |
dc.references | V. Ene, Real functions—Current Topics, Lecture Notes in Mathematics 1603, Springer, Berlin, 1995 | pl_PL |
dc.references | V. Ene, Hake–Alexandroff–Looman type theorems, Real Anal. Exchange 23 (1997/98), 491–524. | pl_PL |
dc.references | V. Ene, Characterizations of VBG\(N), Real Anal. Exchange 23 (1997/98), 611–630. | pl_PL |
dc.references | V. Ene, Thomson’s variational measure, Real Anal. Exchange 24 (1998/99), 523–565. | pl_PL |
dc.references | V. Ene, Thomson’s variational measure and nonabsolutely convergent integrals, Real Anal. Exchange 26 (2000/01), 35–49. | pl_PL |
dc.references | V. Ene, A study of some general integrals that contains the wide Denjoy integral, Real Anal. Exchange 26 (2000/01), 51–100. | pl_PL |
dc.references | C.-A. Faure, A descriptive definition of the KH-Stieltjes integral, Real Anal. Exchange 23 (1997/98), 113–124. | pl_PL |
dc.references | C. Freiling, D. Rinne, A symmetric density property for measurable sets, Real Anal. Exchange 14 (1988/89), 203–209. | pl_PL |
dc.references | S. S. Fu, An ACG function which is not an ACGS-function, Real Anal. Exchange 19 (1993/94), 274–277. | pl_PL |
dc.references | S. S. Fu, The S-Henstock integration and the approximately strong Lusin condition, Real Anal. Exchange 19 (1993/94), 312–316. | pl_PL |
dc.references | S. S. Fu, An extension of the Foran integral, Proceedings of the American Mathematical Society 123 (1995), 403–404. | pl_PL |
dc.references | R. A. Gordon, The inversion of approximate and dyadic derivatives using an extension of the Henstock integral, Real Anal. Exchange 16 (1990/91), 154–168. | pl_PL |
dc.references | R. A. Gordon, The integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics 4, American Mathematical Society, Providence, 1994. | pl_PL |
dc.references | R. A. Gordon, Some comments on an approximately continuous Khintchine integral, Real Anal. Exchange 20 (1994/95), 831–841. | pl_PL |
dc.references | R. Henstock, Linear Analysis, Butterworths, London, 1967. | pl_PL |
dc.references | J. Jarník, J. Kurzweil, A general form of the product integral and linear ordinary differential equations, Czechoslovak Mathematical Journal 37(112) (1987), 642–659. | pl_PL |
dc.references | A. Khintchine, Sur une extension de l’intégrale de M. Denjoy, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 162 (1916), 287–291. | pl_PL |
dc.references | Y. Kubota, On the approximately continuous Denjoy integral, Tôhoku Mathematical Journal 15 (1963), 253–264. | pl_PL |
dc.references | Y. Kubota, An integral of the Denjoy type, Proceedings of the Japan Academy 40 (1964), 713–717. | pl_PL |
dc.references | Y. Kubota, An integral of the Denjoy type. II, Proceedings of the Japan Academy 42 (1966), 737–742. | pl_PL |
dc.references | Y. Kubota, A characterization of the approximately continuous Denjoy integral, Canadian Journal of Mathematics 22 (1970), 219–226. | pl_PL |
dc.references | C.-M. Lee, A symmetric approximate Perron integral for the coefficient problem of convergent trigonometric series, Real Anal. Exchange 16 (1990/91), 329–339. | pl_PL |
dc.references | C.-M. Lee, Kubota’s AD-integral is more general than Burkill’s AP-integral, Real Anal. Exchange 22 (1996/97), 433–436. | pl_PL |
dc.references | T.-Y. Lee, P.-Y. Lee, The Kubota integral II, Mathematica Japonica 42 (1995), 257–263. | pl_PL |
dc.references | K. Liao, On the descriptive definition of the Burkill approximately continuous integral, Real Anal. Exchange 18 (1992/93), 253–260. | pl_PL |
dc.references | K. Liao, Two types of absolute continuity used in Henstock and AP integration are equivalent, Real Anal. Exchange 19 (1993/94), 212–217. | pl_PL |
dc.references | K. Liao, T. S. Chew, The descriptive definitions and properties of the AP integral and their application to the problem of controlled convergence, Real Anal. Exchange 19 (1993/94), 81–97. | pl_PL |
dc.references | S. Lu, Notes on the approximately continuous Henstock integral, Real Anal. Exchange 22 (1996/97), 377–381. | pl_PL |
dc.references | N. N. Lusin, Sur les propriétés de l’intégrale de M. Denjoy, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 155 (1912), 1475–1477. | pl_PL |
dc.references | N. N. Lusin, Integral and Trigonometric Series, PhD thesis, Moscow, 1915 (in Russian). | pl_PL |
dc.references | K. M. Ostaszewski, Henstock integration in the plane, Memoirs of the American Mathematical Society 353, American Mathematical Society, Providence, 1986. | pl_PL |
dc.references | W. F. Pfeffer, The Riemann Approach to Integration, Cambridge Tracts in Mathematics 109, Cambridge University Press, Cambridge, 1993. | pl_PL |
dc.references | D. Preiss, B. S. Thomson, The approximate symmetric integral, Canadian Journal of Mathematics 41 (1989), 508–555. | pl_PL |
dc.references | J. Ridder, Über approximativ stetige Denjoy-Integrale, Fundamenta Mathematicae 21 (1933), 1–10. | pl_PL |
dc.references | J. Ridder, Über die gegenseitigen Beziehungen verschiedener approximativ stetiger Denjoy–Perron Integrale, Fundamenta Mathematicae 22 (1934), 136–162. | pl_PL |
dc.references | D. N. Sarkhel, A wide Perron integral, Bulletin of the Australian Mathematical Society 34 (1986), 233–251. | pl_PL |
dc.references | D. N. Sarkhel, A wide constructive integral, Mathematica Japonica 32 (1987), 295–309. | pl_PL |
dc.references | D. N. Sarkhel, On the approximately continuous integrals of Burkill and Kubota, Real Anal. Exchange 23 (1997/98), 735–742. | pl_PL |
dc.references | D. N. Sarkhel, A. B. Kar, [PVB] functions and integration, Journal of the Australian Mathematical Society (Series A) 36 (1984), 335–353. | pl_PL |
dc.references | S. Saks, Theory of Integral, G. E. Stechert & Co., New York, 1937. | pl_PL |
dc.references | V. A. Skvortsov, Approximate symmetric variation and Luzin’s N-property, Izvestiya Rossiiskoı Akademii Nauk, Ser. Mat. 61 (1997), 155–166 (in Russian). | pl_PL |
dc.references | V. A. Skvortsov, A variational measure and sufficient conditions for the differentiability of an additive interval function, Vestnik Moskovskogo Universiteta, Ser. 1 Mat. Mech. 52 (1997), 55–57 (in Russian). | pl_PL |
dc.references | V. A. Skvortsov, P. Sworowski, The AP-Denjoy and AP-Henstock integrals revisited, Czechoslovak Mathematical Journal 62(137) (2012), 581—591. | pl_PL |
dc.references | V. A. Skvortsov, B. S. Thomson, Symmetric integrals do not have the Marcinkiewicz property, Real Anal. Exchange 21 (1995/96), 510-–520. | pl_PL |
dc.references | W. Skworcow, P. Sworowski, Generalized Integrals, Uniwersytet Kazimierza Wielkiego, Bydgoszcz, 2010 (in Polish). | pl_PL |
dc.references | B. Soedijono, P.-Y. Lee, The Kubota integral, Mathematica Japonica 36 (1991), 263–270. | pl_PL |
dc.references | T. A. Sworowska, Recovering a function from its trigonometric integral, Matematicheskii Sbornik 201 (2010), 1053–1068. | pl_PL |
dc.references | P. Sworowski, An answer to some questions of Ene, Real Anal. Exchange 30 (2004/05), 183–192. | pl_PL |
dc.references | P. Sworowski, On the approximately continuous Foran integral: completing our chart, Real Anal. Exchange 33 (2007/08), 29–40. | pl_PL |
dc.references | P. Sworowski, Riemann-type definition for the wide Denjoy integral, Rendiconti del Seminario Matematico della Università di Padova 126 (2011), 175–200. | pl_PL |
dc.references | P. Sworowski, V. A. Skvortsov, Variational measure defined by approximate differential basis, Vestnik Moskovskogo Universiteta, Ser. 1 Mat. Mech. 57 (2002), 54–57 (in Russian). | pl_PL |
dc.references | B. S. Thomson, Derivation bases on the real line, Real Anal. Exchange 8 (1982), 67–207, 278–442. | pl_PL |
dc.references | B. S. Thomson, Real Functions, Lecture Notes in Mathematics 1170, Springer, Berlin, 1985. | pl_PL |
dc.references | G. P. Tolstov, Sur quelques propriétés des fonctions approximativement continues, Mat. Sbornik 5(47) (1939), 637–645. | pl_PL |
dc.references | G. P. Tolstov, Sur l’intégrale de Perron, Matematicheskii Sbornik 5(47) (1939), 647–659. | pl_PL |
dc.references | C. S. Wang, C. S. Ding, An integral involving Thomson’s local systems, Real Anal. Exchange 19 (1993), 248–253. | pl_PL |
dc.references | A. Zygmund, Trigonometric Series, Cambridge University Press, London, 1968. | pl_PL |
dc.contributor.authorEmail | vaskvor2000@yahoo.com | pl_PL |
dc.contributor.authorEmail | tsworowska@versita.com | pl_PL |
dc.contributor.authorEmail | piotrus@ukw.edu.pl | pl_PL |
dc.identifier.doi | 10.18778/7525-971-1.15 | |