We present a proof of the theorem on countability of the set of points of generalized discontinuity of and $(\mathcal{S}$, $\mathcal{Y}$-regular real function$f\colon X \to \mathbb{R}$, where $(\mathcal{S}$ is a local system in $X$ and$\mathcal{Y}$ is a partition of $X$.We start with a definition of a local system in a generalized form and with basic properties of local systems.The concepts are illustrated with examples.The main result is applied both for regularities in the sense of density connectedwith the Lebesgue measure on $\mathbb{R}^n$ (Lebesgue density) and with Baire category ($\mathcal{I}$-density), respectively.
@article{219,
title = {Generalized discountinuity of real-valued funtions},
journal = {Tatra Mountains Mathematical Publications},
volume = {55},
year = {2013},
doi = {10.2478/tatra.v55i0.219},
language = {EN},
url = {http://dml.mathdoc.fr/item/219}
}
Zduńczyk, Rafał. Generalized discountinuity of real-valued funtions. Tatra Mountains Mathematical Publications, Tome 55 (2013) . doi : 10.2478/tatra.v55i0.219. http://gdmltest.u-ga.fr/item/219/