Pointwise Limits of Sequences of Right-Continuous Functions and Measurability of Functions of Two Variables

In this article I prove that the pointwise limit $f\colon\mathbb R \to \mathbb R$ of a sequence of right-continuous functions has some special property (G) and that bounded functions of two variables $g\colon\mathbb R^2 \to \mathbb R$ whose vertical sections $g_x$, $x\in \mathbb R$, are derivatives and horizontal sections $g^y$, $y\in \mathbb R$, are pointwise limits of sequences of right-continuous functions, are measurable and sup-measurable in the sense of Lebesgue.