$\lambda$-power integrals on the Cantor type sets
HTML articles powered by AMS MathViewer
- by Shushang Fu PDF
- Proc. Amer. Math. Soc. 123 (1995), 2731-2737 Request permission
Abstract:
We introduce the notions of $\lambda$-power dyadic derivatives and $\lambda$-power dyadic integrals, so that, in particular, the Cantor ternery function is an indefinite integral of its derivative. Furthermore, under certain conditions on the integrands we can give a Riemann-type definition to the $\lambda$-power dyadic integral.References
- Russell A. Gordon, The inversion of approximate and dyadic derivatives using an extension of the Henstock integral, Real Anal. Exchange 16 (1990/91), no.Β 1, 154β168. MR 1087481, DOI 10.2307/44153686 J. Kahane, Une theorie de Denjoy des martingales dyadiques, Prepublication from Unite Associee CNRS757, Universite de Paris-Sud.
- Peng Yee Lee, Lanzhou lectures on Henstock integration, Series in Real Analysis, vol. 2, World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. MR 1050957, DOI 10.1142/0845 A. Pacquenaent, Determination dβune fonction a moyen de sa derivee sur un resean binaire, C. R. Acad. Sci. Paris Ser. A 284 (1977), 365-368.
- Brian S. Thomson, Derivates of interval functions, Mem. Amer. Math. Soc. 93 (1991), no.Β 452, vi+96. MR 1078198, DOI 10.1090/memo/0452
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2731-2737
- MSC: Primary 26A24; Secondary 26A39
- DOI: https://doi.org/10.1090/S0002-9939-1995-1257105-3
- MathSciNet review: 1257105