On discrete limits of sequences of functions satisfying some special approximate quasicontinuity conditions (Q1852325)

For \(f_n: \mathbb{R}\to\mathbb{R}\), \(f:\mathbb{R}\to \mathbb{R}\), we say according to the \textit{Á. Császár} and \textit{M. Laczkovich} [Stud. Sci. Math. Hung. 10, 463-472 (1975; Zbl 0405.26006)] that \(f\) is the discrete limit of \(f_n\) iff, for each \(x\in\mathbb{R}\), there is \(k\in\mathbb{N}\) such that \(f_n(x)= f(x)\) whenever \(n> k\). The author has introduced [in Real Anal. Exch. 24, No. 1, 171-183 (1998; Zbl 0940.26003)] quasicontinuity conditions \((s_1)\) to \((s_4)\) for functions \(f:\mathbb{R}\to\mathbb{R}\). The purpose of the present paper is to formulate properties of discrete limits of sequences satisfying \((s_1)\) to \((s_4)\) (e.g., \(f\) is the discrete limit of a sequence of functions satisfying \((s_3)\) iff it is measurable).