Theory of air pollution damage on human populations

Existing ideas of dose or exposure are discussed and criticized from the view point of the health damage caused by time dependent air pollutant concentrations. The idea of "dosage" is introduced and some of its mathematical properties are shown and illustrated. The problem of whether or not there exists threshold concentration in air pollution, as well as that of the relation between equi-exposure and equi-damage, is then discussed by making use of the ideas of dosage and healing power of the population. The assumption of this discussion is that the statistical distribution of air pollutant concentrations is log-normal, and that its time series is stationary.