  This paper builds on a recent article co-authored by the present author, H.
Hosni and F. Montagna. It is meant to contribute to the logical foundations of
probability theory on many-valued events and, specifically, to a deeper
understanding of the notion of strict coherence. In particular, we will make
use of geometrical, measure-theoretical and logical methods to provide three
characterizations of strict coherence on formulas of infinite-valued
{\L}ukasewicz logic
