  We show that it is possible to solve the cosmological constant (CC) problem
in a discrete quantum gravity theory based on Regge calculus by using the
effective action approach and a special path-integral measure. The effective
cosmological constant is given as a sum of 3 terms: the classical CC, the
quantum gravity CC and the matter CC. Since the observations can only measure
the sum of these 3 terms, we can choose the classical CC to be equal to the
negative value of the matter CC. Hence the effective CC is given only by the
quantum gravity CC, which is determined by the path-integral measure. Since the
path-integral measure depends on a free parameter, this parameter can be chosen
such that the effective CC gives the observed value.
