The space of the strong Świątkowski functions

Rok, strany: 2004, 35 - 42

The definition of a strong Świątkowski property for a function $f : [a,b] ightarrow Bbb R$ at a fixed point of $[a,b]$ has been formulated in the paper [J. Kucner, R. J. Pawlak: On local characterization of the strong Świątkowski property for a function $f:[a,b ] ightarrow Bbb R$, Real Anal. Exchange 28 (2003), 563–572]. Theorem 11 presented in that paper seems to suggest the question connected with comparisons of the class of strong Świątkowski functions with the Baire class one. In this paper we give some answers to this question. In particular, we prove that in the space of bounded strong Świątkowski functions (with the metric of uniform convergence) a set $L$ of all functions measurable (in the Lebesgue sense) is a superporous set at each point of this space.

ISO 690:

Kucner, J. 2004. The space of the strong Świątkowski functions. In Tatra Mountains Mathematical Publications, vol. 28, no.1, pp. 35-42. 1210-3195.

APA:

Kucner, J. (2004). The space of the strong Świątkowski functions. Tatra Mountains Mathematical Publications, 28(1), 35-42. 1210-3195.