Let (X,B) be a log canonical pair over a normal variety Z with maximal
Albanese dimension. If KX+B is relatively abundant over Z (for example,
KX+B is relatively big over Z), then we prove that KX+B is abundant. In
particular, the subadditvity of Kodaira dimensions κ(KX+B)≥κ(KF+BF)+κ(Z) holds, where F is a general fiber, KF+BF=(KX+B)∣F, and κ(Z) means the Kodaira dimension of a smooth model of
Z. We discuss several variants of this result in Section 4. We also give a
remark on the log Iitaka conjecture for log canonical pairs in Section 5.Comment: 24 pages. Some typos fixe