Average magnification effect of clumping of matter

The aim of this paper is to reexamine the question of the average magnification in a universe with some inhomogeneously distributed matter. We present an analytic proof, valid under rather general conditions, including clumps of any shape and size, and strong lensing, that so long as the clumps are uncorrelated the average reciprocal magnification (in only one of at least four possible meanings of the words) is precisely the same as in a homogeneous universe with equal mean density. We also discuss, in the context of observations of discrete and extended sources, the physical significance of the various different measures of magnification and the circumstances in which they are appropriate. The interpretation of quasar, type 1A supernovae and cosmic microwave background data could be significantly biased if the wrong measure is employed.