The article [Reference Nešetřil and de Mendez2] deals with the existence of totally Borel limits, i.e., modelings, for FO-converging sequences of graphs. It is shown there that for monotone classes of graphs (i.e., classes closed on subgraphs) this existence is equivalent to nowhere density. The crucial step in this result is formulated there as Theorem 3.2 and deals with existence modelings for $\textsf {FO}_1$ converging sequences. The proof in [Reference Nešetřil and de Mendez2] is based on the Friedman’s $Q_m$ -logic, but there is a flaw in its proof. Shortly, the proof needs that the limit measure on the Stone space is absolutely continuous with respect to the measure produced by Friedman’s construction. However, this is not true in general. Theorem 3.2 and its Corollary 3.3 may still be valid, but for now, the conjecture that every convergent residual sequence of finite structures admits a modeling limit (stated as Conjecture 1.1 in [Reference Nešetřil and de Mendez2]) remains open.

An alternative approach to the main conjecture addressed in [Reference Nešetřil and de Mendez2] (that a monotone class of graphs admits modeling limits if and only if it is nowhere dense, Conjecture 1.2 in [Reference Nešetřil and de Mendez2]) is proposed in [Reference Braunfeld, Nešetřil and de Mendez1], where we claim an even stronger result: every hereditary stable class of structures admits modeling limits.