  Early in 1970s, Carlson-Griffiths made a significant progress in the study of
Nevanlinna theory, who devised equi-distribution theory for holomorphic
mappings from $\mathbb C^m$ into a projective algebraic manifold intersecting
divisors. In this paper, we develop Carlson-Griffiths' theory by generalizing
the source manifold $\mathbb C^m$ to complete K\"ahler manifolds.
