This paper tackles the issue of interpreting the number of airborne particles adsorbed on a filter through which a certain volume of sampled air has been pumped. This number is equal to the product of the pumped volume and particle concentration in air, but only if the concentration is constant over time and if there is no substance decomposition on the filter during sampling. If this is not the case, one must take into account the inconstancy of the concentration and the decay law for a given substance, which is complicated even further if the flow rate through the filter is not constant. In this paper, we develop a formalism which considers all of these factors, resulting in a single, compact expression of general applicability. The use of this expression is exemplified by addressing a case of sampling airborne radioactive matter, where the decay law is already well known. This law is combined with three experimentally observed time dependence of the flow rate and two models for the time dependence of the particle concentration. We also discuss the implications of these calculations for certain other situations of interest to environmental studies.