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Let $f:X\rightarrow Y$ be an algebraic fibre space between normal projectivevarieties and $F$ be a general fibre of $f$. We prove an Iitaka-type inequality$\kappa(X,-K_X)\leq \kappa(F,-K_F)+\kappa(Y,-K_Y)$ under some mild conditions.We also obtain some more results relates the positivity of $-K_X$ and $-K_Y$.

Positivity of anticanonical divisors in algebraic fibre spaces