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## A general differentiation theorem for multiparameter additive processes

### Tom 91 / 2002

Colloquium Mathematicum 91 (2002), 143-155 MSC: Primary 47A35, 47D03, 46E30. DOI: 10.4064/cm91-1-10

#### Streszczenie

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 $T$.

#### Autorzy

• Ryotaro SatoDepartment of Mathematics
Faculty of Science
Okayama University
Okayama, 700-8530 Japan
e-mail

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