Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds

The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting an arbitrary family of hypersurfaces with explicit truncation level. In our result, both the total defect and the truncation level are estimated independently of the number of involving hypersurfaces. Our result generalizes and improves the previous results in this topic.