$ω$-primitives on $σ$-discrete metric spaces

Rok, strany: 2002, 13 - 27

This paper continues the investigation started in [Z. Duszyński, Z. Grande, S. P. Ponomarev: On the $ω$-primitive, Math. Slovaca, 51 (2001), 469–476], [J. Ewert, S. P. Ponomarev: Oscillation and $ω$-primitives, Real Anal. Exchange, 26 (2000–2001), 687–702], [P. Kostyrko: Some properties of oscillation, Math. Slovaca, 30 (1980), 157–162], in the case of $σ$-discrete metric spaces. It is shown that given an upper semicontinuous function $f:X o [0,∞]$, where $X$ is a $σ$-discrete dense in itself metric space, there exists a function $F:X o Bbb R$ (called an $ω$-primitive for $f$) whose oscillation equals $f$.

ISO 690:

Ewert, J., Ponomarev, S. 2002. $ω$-primitives on $σ$-discrete metric spaces. In Tatra Mountains Mathematical Publications, vol. 24, no.1, pp. 13-27. 1210-3195.

APA:

Ewert, J., Ponomarev, S. (2002). $ω$-primitives on $σ$-discrete metric spaces. Tatra Mountains Mathematical Publications, 24(1), 13-27. 1210-3195.