On variations of functions of one real variable

Washek Frank Pfeffer

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 61-71
  • ISSN: 0010-2628

Abstract

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We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.

How to cite

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Pfeffer, Washek Frank. "On variations of functions of one real variable." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 61-71. <http://eudml.org/doc/248057>.

@article{Pfeffer1997,
abstract = {We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.},
author = {Pfeffer, Washek Frank},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lebesgue integral; Denjoy-Perron integral; variational measure; Lebesgue integral; Denjoy-Perron integral; variational measure; gage integral},
language = {eng},
number = {1},
pages = {61-71},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On variations of functions of one real variable},
url = {http://eudml.org/doc/248057},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Pfeffer, Washek Frank
TI - On variations of functions of one real variable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 61
EP - 71
AB - We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.
LA - eng
KW - Lebesgue integral; Denjoy-Perron integral; variational measure; Lebesgue integral; Denjoy-Perron integral; variational measure; gage integral
UR - http://eudml.org/doc/248057
ER -

References

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  1. Bongiorno B., Pfeffer W.F., Thomson B.S., A full descriptive definition of the gage integral, Canadian Math. Bull., in press. Zbl0885.26008MR1426684
  2. Bongiorno B., Di Piazza L., Skvortsov V., A new full descriptive characterization of Denjoy-Perron integral, to appear. Zbl0879.26026
  3. Buczolich Z., Pfeffer W.F., Variations of additive functions, Czechoslovak Math. J., in press. Zbl0903.26004MR1461431
  4. Engelking R., General Topology, PWN, Warsaw, 1977. Zbl0684.54001MR0500780
  5. Gordon R.A., The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Amer. Math. Soc., Providence, 1994. Zbl0807.26004MR1288751
  6. Henstock R., A Riemann type integral of Lebesgue power, Canadian J. Math. 20 (1968), 79-87. (1968) Zbl0171.01804MR0219675
  7. Howard E.J., Analyticity of almost everywhere differentiable functions, Proc. Amer. Math. Soc. 110 (1990), 745-753. (1990) Zbl0705.30001MR1027093
  8. Kurzweil J., Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 82 (1957), 418-446. (1957) Zbl0090.30002MR0111875
  9. Kurzweil J., Jarník J., Differentiability and integrability in n dimensions with respect to α -regular intervals, Results Math. 21 (1992), 138-151. (1992) MR1146639
  10. McShane E.J., A unified theory of integration, Amer. Math. Monthly 80 (1973), 349-359. (1973) Zbl0266.26008MR0318434
  11. Novikov A., Pfeffer W.F., An invariant Riemann type integral defined by figures, Proc. Amer. Math. Soc. 120 (1994), 849-853. (1994) MR1182703
  12. Pfeffer W.F., The Riemann Approach to Integration, Cambridge Univ. Press, New York, 1993. Zbl1143.26005MR1268404
  13. Pfeffer W.F., Lectures on geometric integration and the divergence theorem, Rend. Mat. Univ. Trieste 23 (1991), 263-314. (1991) Zbl0789.26007MR1248655
  14. Rudin W., Real and Complex Analysis, McGraw-Hill, New York, 1987. Zbl1038.00002MR0924157
  15. Thomson B.S., Derivatives of Interval Functions, Mem. Amer. Math. Soc., #452, Providence, 1991. MR1078198

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