This is the last in a series of three communications on the linear response theory of the scanning tunneling microscope (STM). In the first we presented the formal phenomenological theory and applied it to the study of the effect of finite response times on measurements performed with scanning instruments. In the second paper, we discussed the semi-empirical determination of the instrument function representing the blurring and broadening of the ideal measurements by the real instrument. The instrument function is applied in the solution of the inverse problem posed by the interpretation of the STM measurements. In the present communication, the lateral and generalized normal resolutions of the STM are studied in terms of the linear response theory of measurement. This is the first general first-principles discussion of resolution for the STM. The resolution is related to the degradation of the measured data which manifests itself in the fuzziness and distortion of images. The resolution is also affected by the fluctuations in the measured data. The former lead to contrast reduction, the latter limits the detectability. The generalized cutoff “frequency” of measurement instruments and “ O m-resolving power” for the measured quantities, O m, are introduced as measures of the lateral and (generalized) normal resolutions. Their interrelation is discussed. The effect of random fluctuations on the determination of the instrument functions is examined. The general analysis is illustrated, in studies of the optimal tip-sample surface separation and of bounds on the lateral resolution, in a simple model.