*Tommaso Flaminio, Lluis Godo*

The notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, β on a finite set of conditional events is stably coherent if there exists a coherent variant β′ of β such that β′ maps all antecedents of conditional events to a strictly positive hyperreal number, and such that β and β′ differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on Łukasiewicz logic events.

**Keywords:** Layers of zero probability, Conditional probability, Stable coherence MV-algebras.

, Volume 21, Issue 1, pp. 113–123.