This paper concerns a generalization of approximately continuous functions, namely $$ \mathcal{S} $$ -approximately continuous functions. This notion is associated with $$ \mathcal{S} $$ -density points, where $$ \mathcal{S} $$ is a sequence of measurable sets tending to 0. Moreover, we present some properties of these functions and show their connection with measurable functions, functions from the first Baire class, and Darboux functions.

中文翻译：

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在 $$ \mathcal{S} $$-近似连续函数上

本文涉及近似连续函数的推广，即 $$ \mathcal{S} $$ -近似连续函数。这个概念与 $$ \mathcal{S} $$ -密度点相关，其中 $$ \mathcal{S} $$ 是趋向于 0 的可测集序列。此外，我们展示了这些函数的一些性质并展示了它们与可测函数、第一类 Baire 函数和 Darboux 函数的连接。