We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.
@article{118902, author = {Washek Frank Pfeffer}, title = {On variations of functions of one real variable}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {61-71}, zbl = {0888.26006}, mrnumber = {1455470}, language = {en}, url = {http://dml.mathdoc.fr/item/118902} }
Pfeffer, Washek Frank. On variations of functions of one real variable. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 61-71. http://gdmltest.u-ga.fr/item/118902/
A full descriptive definition of the gage integral, Canadian Math. Bull., in press. | MR 1426684 | Zbl 0885.26008
A new full descriptive characterization of Denjoy-Perron integral, to appear. | Zbl 0879.26026
Variations of additive functions, Czechoslovak Math. J., in press. | MR 1461431 | Zbl 0903.26004
General Topology, PWN, Warsaw, 1977. | MR 0500780 | Zbl 0684.54001
The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Amer. Math. Soc., Providence, 1994. | MR 1288751 | Zbl 0807.26004
A Riemann type integral of Lebesgue power, Canadian J. Math. 20 (1968), 79-87. (1968) | MR 0219675 | Zbl 0171.01804
Analyticity of almost everywhere differentiable functions, Proc. Amer. Math. Soc. 110 (1990), 745-753. (1990) | MR 1027093 | Zbl 0705.30001
Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 82 (1957), 418-446. (1957) | MR 0111875 | Zbl 0090.30002
Differentiability and integrability in $n$ dimensions with respect to $\alpha $-regular intervals, Results Math. 21 (1992), 138-151. (1992) | MR 1146639
A unified theory of integration, Amer. Math. Monthly 80 (1973), 349-359. (1973) | MR 0318434 | Zbl 0266.26008
An invariant Riemann type integral defined by figures, Proc. Amer. Math. Soc. 120 (1994), 849-853. (1994) | MR 1182703
The Riemann Approach to Integration, Cambridge Univ. Press, New York, 1993. | MR 1268404 | Zbl 1143.26005
Lectures on geometric integration and the divergence theorem, Rend. Mat. Univ. Trieste 23 (1991), 263-314. (1991) | MR 1248655 | Zbl 0789.26007
Real and Complex Analysis, McGraw-Hill, New York, 1987. | MR 0924157 | Zbl 1038.00002
Derivatives of Interval Functions, Mem. Amer. Math. Soc., #452, Providence, 1991. | MR 1078198