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Let $ (\Omega,\mathcal A)$ be a measurable space $ E$ be a $ \mathbb R$ -Banach space $ \mu:\mathcal A\to E$ with $ \mu(\emptyset)=0$ and $ $ \mu\left(\biguplus_{n\in\mathbb N}A_n\right)=\sum_{n\in\mathbb N}\mu(A_n)\tag1$ $ for all disjoint $ (A_n)_{n\in\mathbb N}\subseteq\mathcal A$ Now, let $ $ |\mu|(A):=\sup\left\{\sum_{i=1}^n\left\|\mu(A_i)\right\|_E:n\in\mathbb N\text{ and }A_1,\ldots,A_n\in\mathcal A\text{ are disjoint with }\biguplus_{i=1}^nA_i\subseteq A\right\}$ $ for $Read more