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Abstract

Let $(L,\| \cdot \| _{L})$ be a Banach lattice of equivalence classes of real-valued measurable functions on a $\sigma $-finite measure space and $T=\{ T(u):u=(u_{1}, \dots,u_{d})$, $u_{i}>0$, $1\leq i\leq d\} $ be a strongly continuous locally bounded $d$-dimensional semigroup of positive linear operators on $L$. Under suitable conditions on the Banach lattice $L$ we prove a general differentiation theorem for locally bounded $d$-dimensional processes in $L$ which are additive with respect to the semigroup $T$.