In: Tatra Mountains Mathematical Publications, vol. 55, no. 2
Rafał Zduńczyk
Detaily:
Rok, strany: 2013, 1 - 16
Kľúčové slová:
local system, filtering system, generalized limits, density point, $\mathcal{I}$-density point, lower density
O článku:
We present a proof of the theorem on countability of the set of points of generalized discontinuity of an $(\mathcal{S},\mathcal{Y})$-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 connected with the Lebesgue measure on $\mathbb{R}n$ (Lebesgue density) and with Baire category ($\mathcal{I}$-density), respectively.
Ako citovať:
ISO 690:
Zduńczyk, R. 2013. Generalized discontinuity of real-valued functions. In Tatra Mountains Mathematical Publications, vol. 55, no.2, pp. 1-16. 1210-3195.
APA:
Zduńczyk, R. (2013). Generalized discontinuity of real-valued functions. Tatra Mountains Mathematical Publications, 55(2), 1-16. 1210-3195.