The limiting oscillations of continuous functions - Maslyuchenko, O.V.; Onypa, D.P. (Carpathian Mathematical Publications, 2015)
We prove that for any upper semicontinuous function $f:F\rightarrow [0;+\infty]$ defined on the boundary $F=\overline G\setminus G$ of some open set $G$ in metrizable space $X$ there is a continuous function $g:G\rightarrow \mathbb R$ such that the limiting oscillation $\widetilde \omega_g$ of it equals $f$.