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We reduce Iitaka's subadditivity conjecture for the logarithmic Kodairadimension to a special case of the generalized abundance conjecture byestablishing an Iitaka type inequality for Nakayama's numerical Kodairadimension. Our proof heavily depends on Nakayama's theory of $\omega$-sheavesand $\widehat{\omega}$-sheaves. As an application, we prove the subadditivityof the logarithmic Kodaira dimension for affine varieties by using the minimalmodel program for projective klt pairs with big boundary divisor.

On subadditivity of the logarithmic Kodaira dimension