On a generalized canonical bundle formula for generically finite morphisms

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with ?-coefficients). This complements Filipazzi’s with connected fibres. It is then applied to obtain subadjunction log centers pairs. As another application, we show that image an anti-nef pair has structure numerically trivial pair. readily implies result Chen–Zhang. Along way Shokurov type convex sets divisors are indeed rational polyhedral sets.