  Let K be a field. A positive motivic measure on the Grothendieck ring
K_0(Var_K) is a homomorphism from K_0(Var_K) to the real numbers assigning a
nonnegative value to every variety. In this note we show that the only positive
motivic measures are the counting measures: measures on K_0(Var_{F_q}) which
send a variety to its number of rational points over some fixed finite
extension of F_q.
