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I'm not sure how this translation from integration (green box) to summation (blue box) occurred in the screenshot above. Furthermore, I'm also unsure about the change of $\mathit{v}_k$ into $\mathit{v}(\text{du})$.

The "Eqn (3b)" is referring to $\underset{\mathbb{R}^d}{\int }(1\land |u|)\mathit{v}(\text{du})<\infty$.

Please enlighten me in realizing how these transformations resulted.



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