In a paper of McMullen he considers foliations on a manifold determined by a closed 1-form $\rho$. He says an $L^\infty$ function $f$ is constant on the leaves of the foliation if "$df \wedge \rho = 0$ as a current," and I'm having a hard time unwinding exactly what's happening with the currents (which I'm not very familiar with).
My understanding is that currents are functionals on differential forms, and given a function $f$ we can define a current on $n$-forms (for an $n$-dimensional manifold) by integrating $f$ times the $n$-form. Similarly, the 1-form $\rho$ defines a current on the $(n-1)$-forms by integrating the wedge of the form with $\rho$. But what's going on with $df \wedge \rho$? I get that we can define a differential of a current by $[dT](\omega) = T(d\omega)$, so I guess $df$ refers to the current on $n-1$ forms which sends $\omega \mapsto \int f d\omega$, but how is the wedge with $\rho$ defined?
My only guess is that $df \wedge \rho$ is a current acting on $(n-2)$ forms sending $\omega \mapsto \int f \cdot (d\omega \wedge \rho)$. Even if that's correct, why does $f$ being constant on leaves imply this current is zero? It seems strange to me that functions constant on the leaves of the foliation determined by $\rho$, which have codimension $1$, can be expressed in terms of $n-2$ forms.