  We define a state as a $[0,1]$-valued, finitely additive function attaining
the value $1$ on an EMV-algebra, which is an algebraic structure close to
MV-algebras, where the top element is not assumed. We show that states always
exist, the extremal states are exactly state-morphisms. Nevertheless the state
space is a convex space that is not necessarily compact, a variant of the
Krein--Mil'man theorem saying states are generated by extremal states, is
proved. We define a weaker form of states, pre-states and strong pre-states,
and also Jordan signed measures which form a Dedekind complete $\ell$-group.
Finally, we show that every state can be represented by a unique regular
probability measure, and a variant of the Horn--Tarski theorem is proved.
