A measure theoretic approach to linear inverse atmospheric dispersion problems

Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made. We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimisation method. That is, we derive conditions for when the least-squares problem is well-defined.