Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T04:12:21.129Z Has data issue: false hasContentIssue false
  • English
  • Français

On Characterizing Classes of Functions in Terms of Associated Sets

Published online by Cambridge University Press:  20 November 2018

A. M. Bruckner
A. M. Bruckner*
Affiliation:
University of California, Santa Barbara
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let κ be a class of real valued functions defined on an interval which need not be bounded. The class κ is said to be characterized in terms of associated sets if there exists a family of sets of real numbers P such that f ∈ κ if and only if for every real number α the sets a remembers of P. Many classes of functions have been characterized in terms of associated sets. The chart below summarizes a few such characterizations.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 227 - 231
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Bruckner, A. M., Céder, J. and Weiss, M., On uniform limits of Darboux functions. Colloq. Math. 15 (1966), pages 65-77.Google Scholar
2. Choquet, G., Applications des propriétés descriptive de la fonction contingient à la théorie des fonctions de variable réelle et à la géométrie différentiable des variétés cartésiennes. J. Math. Pures Appl (9) 27 (1944), pages 115-226.Google Scholar
3. Khintchine, A., Recherchessur la structure des fonctions measurables. Fund. Math. 9 (1922), pages 212-279.Google Scholar
4. Khintchine, A., Recherchessur la structure des fonctions measurables. RecuielMathem. 31 (1922), pages 265-285, 377-433 (Russian).Google Scholar
5. Tolstoff, G., Sur quelques propriétés des fonctionsapproximativement continues. Rec. Math. (Mat. Sbornik) NS. 5 (1933), pages 637-645.Google Scholar
6. Weil, C., On properties of derivatives. Trans. Amer. MathSoc. 114 (1966), pages 363-376.Google Scholar
7. Wilkosz, W., Some properties of derivative functions. FundMath. 2 (1922), pages 145-154.Google Scholar
8. Zahorski, Z., Sur la premiére dérivée. Trans Amer. MathSoc. 69 (1955), pages 1-54.Google Scholar