The geometric meaning of the Ahlfors—Shimizu characteristic is the following. The inner integral "dm" is the spherical area of the image of the disc |"z"| ≤ "t", counting multiplicity (that is, the parts of the Riemann sphere covered "k" times are counted "k" times). This area is divided by which is the area of the whole Riemann sphere. The result can be interpreted as the average number of sheets in the covering of the Riemann sphere by the disc |"z"| ≤ "t". Then this average covering number is integrated with respect to "t" with weight 1/"t".