Generalized Discontinuity of Real-Valued Functions

Rafał Zduńczyk

doi:10.2478/tmmp-2013-0014

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Generalized Discontinuity of Real-Valued Functions

Tatra Mountains Mathematical Publications

Volume 55 (2013): Issue 1 (August 2013)

By: Rafał Zduńczyk

Open Access

|Aug 2013

Abstract

We present a proof of the theorem on countability of the set of points of generalized discontinuity of an ( , ) regular real function f:X→ℝ, where is a local system in X and 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 ℝⁿ (Lebesgue density) and with Baire category -density), respectively.

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