  We introduce and study the space of \emph{subset currents} on the free group
$F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite
Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial
F_N$ consisting of at least two points. While ordinary geodesic currents
generalize conjugacy classes of nontrivial group elements, a subset current is
a measure-theoretic generalization of the conjugacy class of a nontrivial
finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic
group. The concept of a subset current is related to the notion of an
"invariant random subgroup" with respect to some conjugacy-invariant
probability measure on the space of closed subgroups of a topological group. If
we fix a free basis $A$ of $F_N$, a subset current may also be viewed as an
$F_N$-invariant measure on a "branching" analog of the geodesic flow space for
$F_N$, whose elements are infinite subtrees (rather than just geodesic lines)
of the Cayley graph of $F_N$ with respect to $A$.
