On indefinite BV-integrals

Donatella Bongiorno; Udayan B. Darji; Washek Frank Pfeffer

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 843-853
  • ISSN: 0010-2628

Abstract

top
We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.

How to cite

top

Bongiorno, Donatella, Darji, Udayan B., and Pfeffer, Washek Frank. "On indefinite BV-integrals." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 843-853. <http://eudml.org/doc/248625>.

@article{Bongiorno2000,
abstract = {We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.},
author = {Bongiorno, Donatella, Darji, Udayan B., Pfeffer, Washek Frank},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {BV integral; absolute continuity; pointwise Lipschitz functions; BV-integral; absolute continuity; pointwise Lipschitz functions},
language = {eng},
number = {4},
pages = {843-853},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On indefinite BV-integrals},
url = {http://eudml.org/doc/248625},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Bongiorno, Donatella
AU - Darji, Udayan B.
AU - Pfeffer, Washek Frank
TI - On indefinite BV-integrals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 843
EP - 853
AB - We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.
LA - eng
KW - BV integral; absolute continuity; pointwise Lipschitz functions; BV-integral; absolute continuity; pointwise Lipschitz functions
UR - http://eudml.org/doc/248625
ER -

References

top
  1. Bongiorno B., Di Piazza L., Preiss D., A constructive minimal integral which includes Lebesgue integrable functions and derivatives, J. London Math. Soc., to appear. Zbl0980.26006
  2. Bruckner A.M., Fleissner R.J., Foran J., The minimal integral which includes Lebesgue integrable functions and derivatives, Coll. Math. 50 (1986), 289-293. (1986) Zbl0604.26006MR0857865
  3. Buczolich Z., Pfeffer W.F., Variations of additive functions, Czechoslovak Math. J. 47 (1997), 525-555. (1997) Zbl0903.26004MR1461431
  4. McShane E.J., A unified theory of integration, Amer. Math. Monthly 80 (1973), 349-359. (1973) Zbl0266.26008MR0318434
  5. Pfeffer W.F., The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. Zbl1143.26005MR1268404
  6. Pfeffer W.F., Comparing variations of charges, Indiana Univ. Math. J. 45 (1996), 643-654. (1996) Zbl0894.26004MR1422100
  7. Pfeffer W.F., On variations of functions of one real variable, Comment. Math. Univ. Carolinae 38.1 (1997), 61-71. (1997) Zbl0888.26006MR1455470

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.