  This article proves a uniform exponential decay estimate for Seiberg-Witten
equations on non-compact 4-manifolds with exact symplectic ends of bounded
geometry. This is an extension of the analysis for asymptotically flat almost
K\"ahler (AFAK) structures by Kronheimer and Mrowka. As an application, we
construct an invariant for smooth foliations without holonomy-invariant
transverse measure, which takes value in the boundary-stable version of the
monopole Floer homology group, without invoking the Eliashberg-Thurston
perturbation.
