# Why $\lambda\equiv\nu(\mathbb{R})$ for compound poisson process?

I've seen this notation $\lambda\equiv\nu(\mathbb{R})$ in the book of Tankov and Cont for compound poisson process. I thought before that $\lambda$ (jump intensity) can be choosen independently of jump measure $\nu$. What does this notation imply?

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If the total jump intensity is finite, it is sometimes convenient to think of a normalized (probability) measure $\nu / \nu(\mathbb{R})$, which represents the conditional distribution of an individual jump. In this case this is true, we can choose $\lambda := \nu(\mathbb{R})$ and the normalized measure $\nu / \nu(\mathbb{R})$ independently. However, in other situations it is more natural not to normalize $\nu$ - and it is indeed impossible if $\nu(\mathbb{R}) = \infty$. So, shortly speaking, this is just the definition of $\lambda$.