General integration and extensions.II

Štefan Schwabik

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 983-1005
  • ISSN: 0011-4642

Abstract

top
This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math. J. 60 (2010), 961–981). Two new general extensions are introduced and studied in the class 𝔗 of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy’s special integral by the method of successive approximation, Math. Jap. 41 (1995), 217–230).

How to cite

top

Schwabik, Štefan. "General integration and extensions.II." Czechoslovak Mathematical Journal 60.4 (2010): 983-1005. <http://eudml.org/doc/196544>.

@article{Schwabik2010,
abstract = {This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math. J. 60 (2010), 961–981). Two new general extensions are introduced and studied in the class $\mathfrak \{T\}$ of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy’s special integral by the method of successive approximation, Math. Jap. 41 (1995), 217–230).},
author = {Schwabik, Štefan},
journal = {Czechoslovak Mathematical Journal},
keywords = {abstract integration; extension of integral; Kurzweil-Henstock integration; abstract integration; extension of integral; Kurzweil-Henstock integration},
language = {eng},
number = {4},
pages = {983-1005},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {General integration and extensions.II},
url = {http://eudml.org/doc/196544},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Schwabik, Štefan
TI - General integration and extensions.II
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 983
EP - 1005
AB - This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math. J. 60 (2010), 961–981). Two new general extensions are introduced and studied in the class $\mathfrak {T}$ of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy’s special integral by the method of successive approximation, Math. Jap. 41 (1995), 217–230).
LA - eng
KW - abstract integration; extension of integral; Kurzweil-Henstock integration; abstract integration; extension of integral; Kurzweil-Henstock integration
UR - http://eudml.org/doc/196544
ER -

References

top
  1. Bongiorno, B., Piazza, L. Di, Skvortsov, V., 10.2307/44152676, Real Anal. Exch. 21 (1995), 656-663. (1995) Zbl0879.26026MR1407278DOI10.2307/44152676
  2. Foran, J., Fundamentals of Real Analysis, Marcel Dekker New York (1991). (1991) Zbl0744.26004MR1201817
  3. Gordon, R. A., The Integrals of Lebesgue, Denjoy, Perron and Henstock, American Mathematical Society Providence (1994). (1994) Zbl0807.26004MR1288751
  4. Kubota, Y., 10.5036/mjiu.29.41, Math. J. Ibaraki Univ. 29 (1997), 41-54. (1997) Zbl0924.26005MR1601363DOI10.5036/mjiu.29.41
  5. Kurzweil, J., Nichtabsolut konvergente Integrale, BSB B. G. Teubner Verlagsgesellschaft Leipzig (1980). (1980) Zbl0441.28001MR0597703
  6. Lee, P.-Y., Lanzhou Lectures on Henstock Integration, World Scientific Singapore (1989). (1989) Zbl0699.26004MR1050957
  7. Lee, P.-Y., Výborný, R., The Integral; An Easy Approach after Kurzweil and Henstock, Cambridge Univ. Press Cambridge (2000). (2000) MR1756319
  8. Nakanishi, S., A new definition of the Denjoy's special integral by the method of successive approximation, Math. Jap. 41 (1995), 217-230. (1995) Zbl0932.26007MR1317766
  9. Saks, S., Theory of the Integral, Hafner New York (1937). (1937) Zbl0017.30004
  10. Schwabik, Š., 10.2478/s12175-009-0160-1, Math. Slovaca 59 (2009), 731-752. (2009) MR2564330DOI10.2478/s12175-009-0160-1
  11. Schwabik, Š., 10.1007/s10587-010-0087-2, Czech. Math. J. 60 (2010), 961-981. (2010) MR2738960DOI10.1007/s10587-010-0087-2
  12. Thomson, B. S., Derivates of Interval Functions, Mem. Am. Math. Soc. 452 (1991). (1991) Zbl0734.26003MR1078198

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.